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Path Components of the Space of (Weighted) Composition Operators on Bergman Spaces Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2021-01-02 Alexander V. Abanin, Le Hai Khoi, Pham Trong Tien
The topological structure of the set of (weighted) composition operators has been studied on various function spaces on the unit disc such as Hardy spaces, the space of bounded holomorphic functions, weighted Banach spaces of holomorphic functions with sup-norm, Hilbert Bergman spaces. In this paper we consider this problem for all Bergman spaces \(A_{\alpha }^p\) with \(p \in (0, \infty )\) and \(
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Essential Normality for Beurling-Type Quotient Modules over Tube-Type Domains Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2021-01-02 Shuyi Zhang
In this note we investigate the essential normality of the Beurling-type quotient module \({\mathcal {D}}:=H^2(\Omega )\ominus \eta H^2(\Omega )\) with an inner function \(\eta \) inside \(A(\Omega )\) over an irreducible tube-type domain \(\Omega \). For the Lie ball (of rank 2), we characterize the essential normality of the corresponding quotient Hardy module and determine its essential spectrum
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Best Constants in Weighted Estimates for Dyadic Shifts Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2021-01-02 Adam Osękowski
We identify the weighted \(L^p\)-norms of shift operators in the context of nonatomic probability spaces equipped with tree-like structures.
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On Functional Representations of Positive Hilbert Space Operators Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2021-01-02 Lajos Molnár, Andriamanankasina Ramanantoanina
In this paper we consider some faithful representations of positive Hilbert space operators on structures of nonnegative real functions defined on the unit sphere of the Hilbert space in question. Those representations turn order relations between positive operators to order relations between real functions. Two of them turn the usual Löwner order between operators to the pointwise order between functions
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Krylov Solvability of Unbounded Inverse Linear Problems Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-12-24 Noè Angelo Caruso, Alessandro Michelangeli
The abstract issue of ‘Krylov solvability’ is extensively discussed for the inverse problem \(Af=g\) where A is a (possibly unbounded) linear operator on an infinite-dimensional Hilbert space, and g is a datum in the range of A. The question consists of whether the solution f can be approximated in the Hilbert norm by finite linear combinations of \(g,Ag,A^2g,\dots \), and whether solutions of this
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Correction to: Higher-order Operators on Networks: Hyperbolic and Parabolic Theory Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-12-17 Federica Gregorio, Delio Mugnolo
In the original version of this article, the $ symbols were misinterpreted as part of the article text and placed in the article as it is.
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Variable Step Mollifiers and Applications Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-11-30 Michael Hintermüller, Kostas Papafitsoros, Carlos N. Rautenberg
We consider a mollifying operator with variable step that, in contrast to the standard mollification, is able to preserve the boundary values of functions. We prove boundedness of the operator in all basic Lebesgue, Sobolev and BV spaces as well as corresponding approximation results. The results are then applied to extend recently developed theory concerning the density of convex intersections.
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Almost Invariant Subspaces of the Shift Operator on Vector-Valued Hardy Spaces Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-11-24 Arup Chattopadhyay, Soma Das, Chandan Pradhan
In this article, we characterize nearly invariant subspaces of finite defect for the backward shift operator acting on the vector-valued Hardy space which is a vectorial generalization of a result of Chalendar–Gallardo–Partington. Using this characterization of nearly invariant subspace under the backward shift we completely describe the almost invariant subspaces for the shift and its adjoint acting
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A Morita Characterisation for Algebras and Spaces of Operators on Hilbert Spaces Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-11-23 G. K. Eleftherakis, E. Papapetros
We introduce the notion of \(\Delta \) and \(\sigma \,\Delta -\) pairs for operator algebras and characterise \(\Delta -\) pairs through their categories of left operator modules over these algebras. Furthermore, we introduce the notion of \(\Delta \)-Morita equivalent operator spaces and prove a similar theorem about their algebraic extensions. We prove that \(\sigma \Delta \)-Morita equivalent operator
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Higher-Order Operators on Networks: Hyperbolic and Parabolic Theory Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-11-17 Federica Gregorio, Delio Mugnolo
We study higher-order elliptic operators on one-dimensional ramified structures (networks). We introduce a general variational framework for fourth-order operators that allows us to study features of both hyperbolic and parabolic equations driven by this class of operators. We observe that they extend to the higher-order case and discuss well-posedness and conservation of energy of beam equations,
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Interpolating Matrices Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-11-12 Alberto Dayan
We extend Carleson’s interpolation theorem to sequences of matrices, by giving necessary and sufficient separation conditions for a sequence of matrices to be interpolating.
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Conjugations in $$L^2(\mathcal {H})$$ L 2 ( H ) Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-10-28 M. Cristina Câmara, Kamila Kliś-Garlicka, Bartosz Łanucha, Marek Ptak
Conjugations commuting with \(\mathbf {M}_z\) and intertwining \(\mathbf {M}_z\) and \(\mathbf {M}_{{\bar{z}}}\) in \(L^2(\mathcal {H})\), where \(\mathcal {H}\) is a separable Hilbert space, are characterized. We also investigate which of them leave invariant the whole Hardy space \(H^2(\mathcal {H})\) or a model space \(K_\Theta =H^2(\mathcal {H})\ominus \Theta H^2(\mathcal {H})\), where \(\Theta
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From Lieb–Thirring Inequalities to Spectral Enclosures for the Damped Wave Equation Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-10-27 David Krejčiřík, Tereza Kurimaiová
Using a correspondence between the spectrum of the damped wave equation and non-self-adjoint Schrödinger operators, we derive various bounds on complex eigenvalues of the former. In particular, we establish a sharp result that the one-dimensional damped wave operator is similar to the undamped one provided that the \(L^1\) norm of the (possibly complex-valued) damping is less than 2. It follows that
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Nuclear Embeddings in Weighted Function Spaces Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-10-23 Dorothee D. Haroske, Leszek Skrzypczak
We study nuclear embeddings for weighted spaces of Besov and Triebel–Lizorkin type where the weight belongs to some Muckenhoupt class and is essentially of polynomial type. Here we can extend our previous results concerning the compactness of corresponding embeddings. The concept of nuclearity was introduced by A. Grothendieck in 1955. Recently there is a refreshed interest to study such questions
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The First Szegö Theorem for the Bergman–Toeplitz Matrix Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-10-19 Yongning Li, Ziliang Zhang, Xianfeng Zhao, Dechao Zheng
In this paper, we study the asymptotic behavior of the determinants of Bergman–Toeplitz matrices with symbols in \(H^{\infty }({\mathbb {D}})+C(\overline{{\mathbb {D}}})\). We establish a criterion of the asymptotic invertibility and an asymptotic inversion formula for Bergman–Toeplitz operators. These results are applied to obtain two versions of the first Szegö theorem for Bergman–Toeplitz matrices
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Non-Archimedean Radial Calculus: Volterra Operator and Laplace Transform Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-10-09 Anatoly N. Kochubei
In an earlier paper (A. N. Kochubei, Pacif. J. Math. 269 (2014), 355–369), the author considered a restriction of Vladimirov’s fractional differentiation operator \(D^\alpha \), \(\alpha >0\), to radial functions on a non-Archimedean field. In particular, it was found to possess such a right inverse \(I^\alpha \) that the appropriate change of variables reduces equations with \(D^\alpha \) (for radial
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Isomorphic Well-Posedness of the Final Value Problem for the Heat Equation with the Homogeneous Neumann Condition Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-10-08 Jon Johnsen
This paper concerns the final value problem for the heat equation subjected to the homogeneous Neumann condition on the boundary of a smooth open set in Euclidean space. The problem is here shown to be isomorphically well posed in the sense that there exists a linear homeomorphism between suitably chosen Hilbert spaces containing the solutions and the data, respectively. This improves a recent work
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Generalized Schur–Nevanlinna functions and their realizations Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-10-03 Lassi Lilleberg
Pontryagin space operator valued generalized Schur functions and generalized Nevanlinna functions are investigated by using discrete-time systems, or operator colligations, and state space realizations. It is shown that generalized Schur functions have strong radial limit values almost everywhere on the unit circle. These limit values are contractive with respect to the indefinite inner product, which
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Generalized Multipliers for Left-Invertible Operators and Applications Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-09-21 Paweł Pietrzycki
Generalized multipliers for a left-invertible operator T, whose formal Laurent series \(U_x(z)=\sum _{n=1}^\infty (P_ET^{n}x)\frac{1}{z^n}+\sum _{n=0}^\infty (P_E{T^{\prime *n}}x)z^n\), \(x\in \mathcal {H}\) actually represent analytic functions on an annulus or a disc are investigated. We show that they are coefficients of analytic functions and characterize the commutant of some left-invertible operators
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Equivalence After Extension and Schur Coupling for Relatively Regular Operators Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-08-26 S. ter Horst, M. Messerschmidt, A. C. M. Ran
It was recently shown in Ter Horst et al. (Bull Lond Math Soc 51:1005–1014, 2019) that the Banach space operator relations Equivalence After Extension (EAE) and Schur Coupling (SC) do not coincide by characterizing these relations for operators acting on essentially incomparable Banach spaces. The examples that prove the non-coincidence are Fredholm operators, which is a subclass of relatively regular
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Functional Models of Operators and Their Multivalued Extensions in Hilbert Space Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-08-09 Damir Z. Arov, Harry Dym
This paper presents the first part of a study of functional models of selfadjoint and nonselfadjoint extensions \(\widetilde{A}\) of symmetric and nonsymmetric operators A in a Hilbert space \(\mathfrak {H}\). The extensions will be considered in the framework of linear relations (which may also be interpreted as the graphs of multivalued operators) that are required to have a nonempty set of regular
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Invariant Subspaces for Certain Tuples of Operators with Applications to Reproducing Kernel Correspondences Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-08-06 Baruch Solel
The techniques developed by Popescu, Muhly-Solel and Good for the study of algebras generated by weighted shifts are applied to generalize results of Sarkar and of Bhattacharjee-Eschmeier-Keshari-Sarkar concerning dilations and invariant subspaces for commuting tuples of operators. In that paper the authors prove Beurling-Lax-Halmos type results for commuting tuples \(T=(T_1,\ldots ,T_d)\) of operators
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Laplace–Carleson Embeddings on Model Spaces and Boundedness of Truncated Hankel and Toeplitz Operators Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-08-01 Jonathan R. Partington, Sandra Pott, Radosław Zawiski
A characterisation is given of bounded embeddings from weighted \(L^2\) spaces on bounded intervals into \(L^2\) spaces on the half-plane, induced by isomorphisms given by the Laplace transform onto weighted Hardy and Bergman spaces (Zen spaces). As an application necessary and sufficient conditions are given for the boundedness of truncated Hankel and Toeplitz integral operators, including the weighted
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Some Convergence Theorems for Operator Sequences Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-07-30 Heybetkulu Mustafayev
Let A, T, and B be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences \(\left\{ A^{n}TB^{n}\right\} \) and \(\left\{ \frac{1}{n}\sum _{i=0}^{n-1}A^{i}TB^{i} \right\} \). These results are applied to the Toeplitz, composition, and model operators. Some related problems are
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Representing Kernels of Perturbations of Toeplitz Operators by Backward Shift-Invariant Subspaces Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-07-27 Yuxia Liang, Jonathan R. Partington
It is well known the kernel of a Toeplitz operator is nearly invariant under the backward shift \(S^*\). This paper shows that kernels of finite rank perturbations of Toeplitz operators are nearly \(S^*\)-invariant with finite defect. This enables us to apply a recent theorem by Chalendar–Gallardo–Partington to represent the kernel in terms of backward shift-invariant subspaces, which we identify in
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Invariant Subspaces of the Integration Operators on Hörmander Algebras and Korenblum Type Spaces Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-07-27 José Bonet, Antonio Galbis
We describe the proper closed invariant subspaces of the integration operator when it acts continuously on countable intersections and countable unions of weighted Banach spaces of holomorphic functions on the unit disc or the complex plane. Applications are given to the case of Korenblum type spaces and Hörmander algebras of entire functions.
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Order Isomorphisms on Order Intervals of Atomic JBW-Algebras Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-07-13 Mark Roelands, Marten Wortel
In this paper a full description of order isomorphisms between effect algebras of atomic JBW-algebras is given. We will derive a closed formula for the order isomorphisms on the effect algebra of type I factors by proving that the invertible part of the effect algebra of a type I factor is left invariant. This yields an order isomorphism on the whole cone, for which a characterisation exists. Furthermore
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Arithmetic–Geometric Mean and Related Submajorisation and Norm Inequalities for $$\tau $$ τ -Measurable Operators: Part II Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-07-09 P. G. Dodds, T. K. Dodds, F. A. Sukochev, D. Zanin
The paper establishes arithmetic–geometric mean and related submajorisation and norm inequalities for \(\tau \)-measurable operators affiliated with a semi-finite von Neumann algebra acting in a separable Hilbert space as an application of the theory of double operator integration.
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Strongly Mixing Convolution Operators on Fréchet Spaces of Entire Functions of a Given Type and Order Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-07-09 Blas M. Caraballo, Vinícius V. Fávaro
We show that convolution operators on certain spaces of entire functions of a given type and order on Banach spaces are strongly mixing with respect to an invariant Borel probability measure with full support (a stronger property than frequent hypercyclicity). Based on results of S. Muro, D. Pinasco and M. Savransky we also show the existence of frequently hypercyclic entire functions of exponential
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Inverse Problem for a Stieltjes String Damped at an Interior Point Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-07-03 Lu Yang, Yongxia Guo, Guangsheng Wei
In this paper, we consider the spectral problem for a Stieltjes string with both ends fixed and with one-dimensional damping at an interior point. We solve an inverse problem of recovering parameters of the Stieltjes string using partial information on the string and partial information on the spectrum. First we prove uniqueness and give an algorithm of recovering the unknown parameters of the string
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Joint Functional Calculus for Definitizable Self-adjoint Operators on Krein Spaces Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-06-30 Michael Kaltenbäck, Nathanael Skrepek
In the present note a spectral theorem for a finite tuple of pairwise commuting, self-adjoint and definitizable bounded linear operators \(A_1,\ldots ,A_n\) on a Krein space is derived by developing a functional calculus \(\phi \mapsto \phi (A_1,\ldots ,A_n)\) which is the proper analogue of \(\phi \mapsto \int \phi \, dE\) in the Hilbert space situation with the common spectral measure E for a finite
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Arithmetic–Geometric Mean and Related Submajorisation and Norm Inequalities for $$\tau $$τ -Measurable operators: Part I Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-06-24 P. G. Dodds, T. K. Dodds, F. A. Sukochev, D. Zanin
The paper establishes arithmetic-geometric mean and related submajorisation and norm inequalities in the general setting of \(\tau \)-measurable operators affiliated with a semi-finite von Neumann algebra.
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Commutant Lifting and Nevanlinna–Pick Interpolation in Several Variables Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-06-13 K. D. Deepak, Deepak Kumar Pradhan, Jaydeb Sarkar, Dan Timotin
This paper concerns a commutant lifting theorem and a Nevanlinna–Pick type interpolation result in the setting of multipliers from vector-valued Drury–Arveson space to a large class of vector-valued reproducing kernel Hilbert spaces over the unit ball in \({\mathbb {C}}^n\). The special case of reproducing kernel Hilbert spaces includes all natural examples of Hilbert spaces like Hardy space, Bergman
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Ambrosetti–Prodi Type Results for Dirichlet Problems of Fractional Laplacian-Like Operators Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-06-04 Anup Biswas, József Lőrinczi
We establish Ambrosetti–Prodi type results for viscosity and classical solutions of nonlinear Dirichlet problems for fractional Laplace and comparable operators. In the choice of nonlinearities we consider semi-linear and super-linear growth cases separately. We develop a new technique using a functional integration-based approach, which is more robust in the non-local context than a purely analytic
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Commutative Algebras Generated by Toeplitz Operators on the Unit Sphere Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-06-04 Maribel Loaiza, Nikolai Vasilevski
The classical result by Brown and Halmos (J Reine Angew Math 213:8–102, 1964) implies that there is no nontrivial commutative \(C^*\)-algebra generated by Toeplitz operators acting on the Hardy space \(H^2(S^1)\), while there are only two commutative Banach algebras. One of them is generated by Toeplitz operators with analytic symbols, and the other one is generated by Toeplitz operators with conjugate
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Spectral Determinants and an Ambarzumian Type Theorem on Graphs Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-06-01 Márton Kiss
We consider an inverse problem for Schrödinger operators on connected equilateral graphs with standard matching conditions. We calculate the spectral determinant and prove that the asymptotic distribution of a subset of its zeros can be described by the roots of a polynomial. We verify that one of the roots is equal to the mean value of the potential and apply it to prove an Ambarzumian type result
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Recovering the Shape of a Quantum Graph Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-06-01 A. Chernyshenko, V. Pivovarchik
Sturm–Liouville problems on simple connected equilateral graphs of \(\le 5\) vertices and trees of \(\le 8\) vertices are considered with Kirchhoff’s and continuity conditions at the interior vertices and Neumann conditions at the pendant vertices and the same potential on the edges. It is proved that if the spectrum of such problem is unperturbed (such as in case of zero potential) then this spectrum
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Products of Toeplitz and Hankel Operators on Fock Spaces Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-05-27 Fugang Yan, Dechao Zheng
In this paper, we characterize bounded Toeplitz product \(T_fT_{g}\) and Hankel product \(H_f^{*}H_g\) on Fock space \(F_{\alpha }^2\) for two polynomials f and g in z and \({\overline{z}}\). As a consequence, we obtain when Toeplitz operator \(T_f\) or Hankel operator \(H_f\) with the polynomial symbol f in z and \({\overline{z}}\) is bounded.
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Green Matrix Estimates of Block Jacobi Matrices II: Bounded Gap in the Essential Spectrum Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-05-23 Jan Janas, Sergey Naboko, Luis O. Silva
This paper provides decay bounds for Green matrices and generalized eigenvectors of block Jacobi operators when the real part of the spectral parameter lies in a bounded gap of the operator’s essential spectrum. The case of the spectral parameter being an eigenvalue is also considered. It is also shown that if the matrix entries commute, then the estimates can be refined. Finally, various examples
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Isometries of Analytic Function Spaces with $$N^{p}$$Np -Derivative Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-05-20 Sei-Ichiro Ueki
We introduce the space of analytic functions on the open unit disk whose derivative has the p-th integrable bounded characteristic on the unit circle. We will give the characterization of a linear isometry of this space. We also characterize the surjective, not necessarily linear, multiplicative isometry of this space.
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On Homotopy Invariants of Tensor Products of Banach Algebras Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-04-13 Alexander Brudnyi
We generalize results of Davie and Raeburn describing homotopy types of the group of invertible elements and of the set of idempotents of the projective tensor product of complex unital Banach algebras. We illustrate our results by specific examples.
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Quaternionic Regularity via Analytic Functional Calculus Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-03-21 Florian-Horia Vasilescu
Let \({\mathbb M}\) be the complexification of the quaternionic algebra \({\mathbb H}\). For each function \(F:U\mapsto {\mathbb M}\), where \(U\subset {\mathbb C}\), we define a transformation \(F_{\mathbb H}:U_{\mathbb H}\mapsto {\mathbb M}\), where \(U_{\mathbb H}\subset {\mathbb H}\) is associated to U, via an elementary functional calculus, using the spectra of quaternions, and characterize those
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On the Properties of Quasi-periodic Boundary Integral Operators for the Helmholtz Equation Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-03-21 Rubén Aylwin, Carlos Jerez-Hanckes, José Pinto
We study the mapping properties of boundary integral operators arising when solving two-dimensional, time-harmonic waves scattered by periodic domains. For domains assumed to be at least Lipschitz regular, we propose a novel explicit representation of Sobolev spaces for quasi-periodic functions that allows for an analysis analogous to that of Helmholtz scattering by bounded objects. Except for Rayleigh-Wood
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Spectral Asymptotics of the Dirichlet Laplacian on a Generalized Parabolic Layer Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-03-17 Pavel Exner, Vladimir Lotoreichik
We perform quantitative spectral analysis of the self-adjoint Dirichlet Laplacian \({\mathsf {H}}\) on an unbounded, radially symmetric (generalized) parabolic layer \({\mathcal {P}}\subset {\mathbb {R}}^3\). It was known before that \({\mathsf {H}}\) has an infinite number of eigenvalues below the threshold of its essential spectrum. In the present paper, we find the discrete spectrum asymptotics
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On the Wandering Property in Dirichlet spaces Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-03-17 Eva A. Gallardo-Gutiérrez, Jonathan R. Partington, Daniel Seco
We show that in a scale of weighted Dirichlet spaces \(D_{\alpha }\), including the Bergman space, given any finite Blaschke product B there exists an equivalent norm in \(D_{\alpha }\) such that B satisfies the wandering subspace property with respect to such norm. This extends, in some sense, previous results by Carswell et al. (Indiana Univ Math J 51(4):931–961, 2002). As a particular instance,
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Furstenberg Boundary of Minimal Actions Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-03-17 Zahra Naghavi
For a countable discrete group \(\Gamma \) and a minimal \(\Gamma \)-space X, we study the notion of \((\Gamma , X)\)-boundary, which is a natural generalization of the notion of topological \(\Gamma \)-boundary in the sense of Furstenberg. We give characterizations of the \((\Gamma , X)\)-boundary in terms of essential or proximal extensions. The characterization is used to answer a problem of Hadwin
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Norms of Weighted Composition Operators with Automorphic Symbol Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-03-16 Mahsa Fatehi, Christopher N. B. Hammond
We determine the norm of a weighted composition operator \(W_{\psi ,\varphi }\), acting on the Hardy space \(H^{2}\) or one of the weighted Bergman spaces \(A_{\alpha }^{2}\), in the case where the composition symbol \(\varphi \) is an automorphism of the unit disk. Furthermore, we characterize all such operators that have maximal norm relative to an upper bound stated in terms of \(\Vert \psi \Vert
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Semigroups of Composition Operators in Analytic Morrey Spaces Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-02-29 Petros Galanopoulos, Noel Merchán, Aristomenis G. Siskakis
Analytic Morrey spaces belong to the class of function spaces which, like BMOA, are defined in terms of the degree of oscillation on the boundary of functions analytic in the unit disc. We consider semigroups of composition operators on these spaces and focus on the question of strong continuity. It is shown that these semigroups behave like on BMOA.
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Spectral Properties of Some Complex Jacobi Matrices Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-02-29 Grzegorz Świderski
We study spectral properties of bounded and unbounded complex Jacobi matrices. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous on some subsets of the complex plane and we provide uniform asymptotics of their generalised eigenvectors. We illustrate our results by considering complex perturbations of real Jacobi matrices belonging to several classes:
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How Small Can a Sum of Idempotents Be? Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-02-24 Harm Bart, Torsten Ehrhardt, Bernd Silbermann
The issue discussed in this paper is: how small can a sum of idempotents be? Here smallness is understood in terms of nilpotency or quasinilpotency. Thus the question is: given idempotents \(p_1,\ldots ,p_n\) in a complex algebra or Banach algebra, is it possible that their sum \(p_1+\cdots +p_n\) is quasinilpotent or (even) nilpotent (of a certain order)? The motivation for considering this problem
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Compact Equivalent Inverse of the Electric Field Integral Operator on Screens Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-02-19 R. Hiptmair, C. Urzúa-Torres
We construct inverses of the variational electric field boundary integral operator up to compact perturbations on orientable topologically simple screens. We describe them as solution operators of variational problems set in low-regularity standard trace spaces. On flat disks these variational problems do not involve the inversion of any non-local operators. This result lays the foundation for operator
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A Subnormal Completion Problem for Weighted Shifts on Directed Trees, II Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-02-11 George R. Exner, Il Bong Jung, Jan Stochel, Hye Yeong Yun
The subnormal completion problem on a directed tree is to determine, given a collection of weights on a subtree, whether the weights may be completed to the weights of a subnormal weighted shift on the directed tree. We study this problem on a directed tree with a single branching point, \(\eta \) branches and the trunk of length 1 and its subtree which is the “truncation” of the full tree to vertices
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The Existence of Singular Traces on Simply Generated Operator Ideals Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-01-31 Albrecht Pietsch
We present direct and self-contained proofs of the existence of singular traces on sufficiently large classes of operator ideals that live on the separable infinite-dimensional real Hilbert space. Our only tool is Banach’s version of the extension theorem of linear forms. Thanks to the use of dyadic representations of operators, all proofs have become straightforward.
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One-Sided Invertibility of Toeplitz Operators on the Space of Real Analytic Functions on the Real Line Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-01-28 M. Jasiczak, A. Golińska
We show that a Toeplitz operator on the space of real analytic functions on the real line is left invertible if and only if it is an injective Fredholm operator, it is right invertible if and only if it is a surjective Fredholm operator. The characterizations are given in terms of the winding number of the symbol of the operator. Our results imply that the range of a Toeplitz operator (and also its
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Closable Hankel Operators and Moment Problems Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-01-27 Christian Berg, Ryszard Szwarc
In a paper from 2016 D. R. Yafaev considers Hankel operators associated with Hamburger moment sequences \(q_n\) and claims that the corresponding Hankel form is closable if and only if the moment sequence tends to 0. The claim is not correct, since we prove closability for any indeterminate moment sequence but also for certain determinate moment sequences corresponding to measures with finite index
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Remarks On Essential Codimension Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-01-23 Jireh Loreaux, P. W. Ng
We look for generalizations of the Brown–Douglas–Fillmore essential codimension result, leading to interesting local uniqueness theorems in KK theory. We also study the structure of Paschke dual algebras.
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The Forward and Backward Shift on the Lipschitz Space of a Tree Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2020-01-14 Rubén A. Martínez-Avendaño, Emmanuel Rivera-Guasco
We initiate the study of the forward and backward shifts on the Lipschitz space of an undirected tree, \(\mathcal {L}\), and on the little Lipschitz space of an undirected tree, \(\mathcal {L}_0\). We determine that the forward shift is bounded both on \(\mathcal {L}\) and on \(\mathcal {L}_0\) and, when the tree is leafless, it is an isometry; we also calculate its spectrum. For the backward shift
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On Compact Perturbations of Hankel Operators and Commutators of Toeplitz and Hankel Operators Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2019-12-09 Yi Yan
Motivated by results in uniform algebras, a distance localization formula in C*-algebras is established in the framework of the Allan–Douglas localization principle, and is used to derive a locality result for products of Hankel operators as compact perturbations of Hankel operators. Using localization and certain QC functions, it is proved that the essential spectrum of the commutator of a Toeplitz
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The Spectral Density of Hankel Operators with Piecewise Continuous Symbols Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2019-11-30 Emilio Fedele
In 1966, H. Widom proved an asymptotic formula for the distribution of eigenvalues of the \(N\times N\) truncated Hilbert matrix for large values of N. In this paper, we extend this formula to Hankel matrices with symbols in the class of piece-wise continuous functions on the unit circle. Furthermore, we show that the distribution of the eigenvalues is independent of the choice of truncation (e.g.
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On the Solvability Complexity Index for Unbounded Selfadjoint and Schrödinger Operators Integr. Equ. Oper. Theory (IF 0.921) Pub Date : 2019-11-21 Frank Rösler
We study the solvability complexity index (SCI) for unbounded selfadjoint operators on separable Hilbert spaces and perturbations thereof. In particular, we show that if the extended essential spectrum of a selfadjoint operator is convex, then the SCI for computing its spectrum is equal to 1. This result is then extended to relatively compact perturbations of such operators and applied to Schrödinger
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