样式: 排序: IF: - GO 导出 标记为已读
-
On Operator Valued Haar Unitaries and Bipolar Decompositions of R-diagonal Elements Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2024-02-26
Abstract In the context of operator valued W \(^*\) -free probability theory, we study Haar unitaries, R-diagonal elements and circular elements. Several classes of Haar unitaries are differentiated from each other. The term bipolar decomposition is used for the expression of an element as vx where x is self-adjoint and v is a partial isometry, and we study such decompositions of operator valued R-diagonal
-
Regular Functions on the Scaled Hypercomplex Numbers Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2024-02-26 Daniel Alpay, Ilwoo Cho
In this paper, we study the regularity of \(\mathbb {R}\)-differentiable functions on open connected subsets of the scaled hypercomplex numbers \(\left\{ \mathbb {H}_{t}\right\} _{t\in \mathbb {R}}\) by studying the kernels of suitable differential operators \(\left\{ \nabla _{t}\right\} _{t\in \mathbb {R}}\), up to scales in the real field \(\mathbb {R}\).
-
Invertibility Criteria for the Biharmonic Single-Layer Potential Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2024-02-22
Abstract While the single-layer operator for the Laplacian is well understood, questions remain concerning the single-layer operator for the Bilaplacian, particularly with regard to invertibility issues linked with degenerate scales. In this article, we provide simple sufficient conditions ensuring this invertibility for a wide range of problems.
-
On Rate of Convergence for Universality Limits Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2024-02-21 Roman Bessonov
-
Discussing Semigroup Bounds with Resolvent Estimates Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2024-02-16 Bernard Helffer, Johannes Sjöstrand, Joe Viola
-
On the Real and Imaginary Parts of Powers of the Volterra Operator Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2024-02-15 Thomas Ransford, Dashdondog Tsedenbayar
We study the real and imaginary parts of the powers of the Volterra operator on \(L^2[0,1]\), specifically their eigenvalues, their norms and their numerical ranges.
-
Regular Ideals, Ideal Intersections, and Quotients Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2024-01-29 Jonathan H. Brown, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff
Let \(B \subseteq A\) be an inclusion of \(C^*\)-algebras. We study the relationship between the regular ideals of B and regular ideals of A. We show that if \(B \subseteq A\) is a regular \(C^*\)-inclusion and there is a faithful invariant conditional expectation from A onto B, then there is an isomorphism between the lattice of regular ideals of A and invariant regular ideals of B. We study properties
-
Indefinite Sturm–Liouville Operators in Polar Form Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2024-01-25 Branko Ćurgus, Volodymyr Derkach, Carsten Trunk
We consider the indefinite Sturm–Liouville differential expression $$\begin{aligned} {\mathfrak {a}}(f):= - \frac{1}{w}\left( \frac{1}{r} f' \right) ', \end{aligned}$$ where \({\mathfrak {a}}\) is defined on a finite or infinite open interval I with \(0\in I\) and the coefficients r and w are locally summable and such that r(x) and \(({\text {sgn}}\,x) w(x)\) are positive a.e. on I. With the differential
-
Some Operator Ideal Properties of Volterra Operators on Bergman and Bloch Spaces Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-12-10 Joelle Jreis, Pascal Lefèvre
We characterize the integration operators \(V_g\) with symbol g for which \(V_g\) acts as an absolutely summing operator on weighted Bloch spaces \(\mathcal {B}^{\beta }\) and on weighted Bergman spaces \(\mathscr {A}^p_\alpha \). We show that \(V_g\) is r-summing on \(\mathscr {A}^p_\alpha \), \(1 \le p <\infty \), if and only if g belongs to a suitable Besov space. We also show that there is no non
-
Phases of Sectorial Operators Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-11-21 Tianqiu Yu, Di Zhao, Li Qiu
-
Denjoy–Wolff Points on the Bidisk via Models Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-11-14 Michael T. Jury, Georgios Tsikalas
Let \(F=(\phi , \psi ):\mathbb {D}^2\rightarrow \mathbb {D}^2\) denote a holomorphic self-map of the bidisk without interior fixed points. It is well-known that, unlike the case with self-maps of the disk, the sequence of iterates $$\begin{aligned} \{F^n:=F\circ F\circ \cdots \circ F\} \end{aligned}$$ needn’t converge. The cluster set of \(\{F^n\}\) was described in a classical 1954 paper of Hervé
-
Decay Rate of $$\varvec{\exp (A^{-1}t)A^{-1}}$$ on a Hilbert Space and the Crank–Nicolson Scheme with Smooth Initial Data Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-11-12 Masashi Wakaiki
This paper is concerned with the decay rate of \(e^{A^{-1}t}A^{-1}\) for the generator A of an exponentially stable \(C_0\)-semigroup on a Hilbert space. To estimate the decay rate of \(e^{A^{-1}t}A^{-1}\), we apply a bounded functional calculus. Using this estimate and Lyapunov equations, we also study the quantified asymptotic behavior of the Crank-Nicolson scheme with smooth initial data. A similar
-
Stability Analysis of a Simple Discretization Method for a Class of Strongly Singular Integral Equations Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-11-12 Martin Costabel, Monique Dauge, Khadijeh Nedaiasl
-
Heat Flow in Polygons with Reflecting Edges Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-11-07 Sam Farrington, Katie Gittins
-
Dyadic Maximal Operators on Martingale Musielak–Orlicz Hardy Type Spaces and Applications Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-11-07 Weisz Ferenc, Guangheng Xie, Dachun Yang
Let \(\varphi :\ [0,1)\times [0,\infty )\rightarrow [0,\infty )\) be a Musielak–Orlicz function and \(q\in (0,\infty ]\). In this article, the authors characterize the martingale Musielak–Orlicz Hardy space \(H_{\varphi }[0,1)\) and the martingale Musielak–Orlicz–Lorentz Hardy space \(H_{\varphi ,q}[0,1)\) via dyadic maximal operators. As applications, the authors prove that the maximal Fejér operator
-
On the Power Set of Quasinilpotent Operators Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-10-12 Youqing Ji, Yuanhang Zhang
For a quasinilpotent operator T on a separable Hilbert space \({\mathcal {H}}\), Douglas and Yang define \(k_x=\limsup \limits _{\lambda \rightarrow 0}\frac{\ln \Vert (\lambda -T)^{-1}x\Vert }{\ln \Vert (\lambda -T)^{-1}\Vert }\) for each nonzero vector x, and call \(\Lambda (T)=\{k_x:x\ne 0\}\) the power set of T. In this paper, we prove that \(\Lambda (T)\) is right closed, that is, \(\sup \sigma
-
An Improved Discrete p-Hardy Inequality Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-09-29 Florian Fischer, Matthias Keller, Felix Pogorzelski
We improve the classical discrete Hardy inequality for \( 1
-
Semiflows, Composition Semigroups, and the Approximation of Dirichlet-to-Neumann Semigroups Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-09-22 Lars Perlich
We present an approximation for the semigroup generated by a multiplicative perturbation of a Dirichlet-to-Neumann operator and more general Poincaré–Steklov operators which are in a certain relation to a generator of a semigroup of composition operators. This approach gives in particular an approximation of the semigroup generated by the classical Dirichlet-to-Neumann operator on a Dini-smooth Jordan
-
(Strongly-)Dunford–Pettis Operators and Narrow Operators Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-09-16 Jinghao Huang, Marat Pliev, Fedor Sukochev
Let \({{\mathcal {M}}}\) be a semifinite von Neumann algebra. We show that an operator T from the predual \(L_1({{\mathcal {M}}},\tau )\) of \({{\mathcal {M}}}\) into a Banach space X is strongly Dunford–Pettis if and only if \(T\circ i: L_1({{\mathcal {M}}},\tau ) \cap {{\mathcal {M}}}\rightarrow _i L_1({{\mathcal {M}}},\tau ) \rightarrow _T X\) is compact. We also show that for a finite measure space
-
Classes of Kernels and Continuity Properties of the Double Layer Potential in Hölder Spaces Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-09-09 Massimo Lanza de Cristoforis
We prove the validity of regularizing properties of the boundary integral operator corresponding to the double layer potential associated to the fundamental solution of a nonhomogeneous second order elliptic differential operator with constant coefficients in Hölder spaces by exploiting an estimate on the maximal function of the tangential gradient with respect to the first variable of the kernel of
-
Approximation of the Spectral Action Functional in the Case of $$\tau $$ -Compact Resolvents Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-09-02 Arup Chattopadhyay, Chandan Pradhan, Anna Skripka
We establish estimates and representations for the remainders of Taylor approximations of the spectral action functional \(V\mapsto \tau (f(H_0+V))\) on bounded self-adjoint perturbations, where \(H_0\) is a self-adjoint operator with \(\tau \)-compact resolvent in a semifinite von Neumann algebra and f belongs to a broad set of compactly supported functions including n-times differentiable functions
-
Representations and Regularity of Vector-Valued Right-Shift Invariant Operators Between Half-Line Bessel Potential Spaces Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-08-25 Chris Guiver, Mark R. Opmeer
Representation and boundedness properties of linear, right-shift invariant operators on half-line Bessel potential spaces (also known as fractional-order Sobolev spaces) as operator-valued multiplication operators in terms of the Laplace transform are considered. These objects are closely related to the input–output operators of linear, time-invariant control systems. Characterisations of when such
-
Hilbert $$C^*$$ -Modules with Hilbert Dual and $$C^*$$ -Fredholm Operators Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-06-30 Vladimir Manuilov, Evgenij Troitsky
We study Hilbert \(C^*\)-modules over a \(C^*\)-algebra A for which the Banach A-dual module carries a natural structure of Hilbert A-module. In this direction we prove that if A is monotone complete, M and N are Hilbert A-modules, M is self-dual, and both \(T:M\rightarrow N\) and its Banach A-dual \(T':N'\rightarrow M'\) have trivial kernels and cokernels then \(M\cong N'\). With the help of this
-
On Exponential Splitting Methods for Semilinear Abstract Cauchy problems Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-05-30 Bálint Farkas, Birgit Jacob, Merlin Schmitz
Due to the seminal works of Hochbruck and Ostermann (Appl Numer Math 53(2–4):323–339, 2005, Acta Numer 19:209–286, 2010) exponential splittings are well established numerical methods utilizing operator semigroup theory for the treatment of semilinear evolution equations whose principal linear part involves a sectorial operator with angle greater than \(\frac{\pi }{2}\) (meaning essentially the holomorphy
-
Questions About Extreme Points Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-05-02 Konstantin M. Dyakonov
We discuss the geometry of the unit ball—specifically, the structure of its extreme points (if any)—in subspaces of \(L^1\) and \(L^\infty \) on the circle that are formed by functions with prescribed spectral gaps. A similar issue is considered for kernels of Toeplitz operators in \(H^\infty \).
-
Quasicentral Modulus and Self-similar Sets: A Supplementary Result to Voiculescu’s Work Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-04-24 Kozo Ikeda, Masaki Izumi
In his recent work, Voiculescu generalized his remarkable formula for the quasicentral modulus of a commuting n-tuple of hermitian operators with respect to the (n, 1)-Lorentz ideal to the case where its spectrum is contained in a Cantor-like self-similar set in a certain class. In this note, we treat general self-similar sets satisfying the open set condition, and obtain lower and upper bounds of
-
Essential Spectrum and Feller Type Properties Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-04-20 Ali BenAmor, Batu Güneysu, Peter Stollmann
We give necessary and sufficient conditions for a regular semi-Dirichlet form to enjoy a new Feller type property, which we call weak Feller property. Our characterization involves potential theoretic as well as probabilistic aspects and seems to be new even in the symmetric case. As a consequence, in the symmetric case, we obtain a new variant of a decomposition principle of the essential spectrum
-
Traces on Operator Ideals Defined over the Class of all Banach Spaces and Related Open Problems Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-04-15 Albrecht Pietsch
-
An Exact Formula for the Number of Negative Eigenvalues for Zigzag Carbon Nanotubes with $$\delta $$ Impurities Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-04-01 Hiroaki Niikuni
-
On the Continuity of Strongly Singular Calderón–Zygmund-Type Operators on Hardy Spaces Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-03-20 Tiago Picon, Claudio Vasconcelos
In this work, we establish results on the continuity of strongly singular Calderón–Zygmund operators of type \(\sigma \) on Hardy spaces \(H^p(\mathbb R^n)\) for \(0
-
A Product Formula for Homogeneous Characteristic Functions Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-03-18 Bhaskar Bagchi, Somnath Hazra, Gadadhar Misra
A bounded linear operator T on a Hilbert space is said to be homogeneous if \(\varphi (T)\) is unitarily equivalent to T for all \(\varphi \) in the group Möb of bi-holomorphic automorphisms of the unit disc. A projective unitary representation \(\sigma \) of Möb is said to be associated with an operator T if \(\varphi (T)= \sigma (\varphi )^* T \sigma (\varphi )\) for all \(\varphi \) in Möb. In this
-
On the Eigenvalues of Spectral Gaps of Elliptic PDEs on Waveguides Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-02-28 Salma Aljawi, Marco Marletta
-
The Coburn Lemma and the Hartman–Wintner–Simonenko Theorem for Toeplitz Operators on Abstract Hardy Spaces Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-01-18 Oleksiy Karlovych, Eugene Shargorodsky
Let X be a Banach function space on the unit circle \({\mathbb {T}}\), let \(X'\) be its associate space, and let H[X] and \(H[X']\) be the abstract Hardy spaces built upon X and \(X'\), respectively. Suppose that the Riesz projection P is bounded on X and \(a\in L^\infty {\setminus }\{0\}\). We show that P is bounded on \(X'\). So, we can consider the Toeplitz operators \(T(a)f=P(af)\) and \(T({\
-
Positive and Negative Eigenfunction Expansion Results for Indefinite Sturm–Liouville Problems Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2023-01-06 Andreas Fleige
For a weight function \(r \in L^1[-1,1]\) with sign change at 0 we consider two indefinite regular Sturm–Liouville problems: \(-f'' = \lambda r f\) with Neumann boundary conditions and \(-(\frac{u'}{r})' = \lambda u\) with Dirichlet boundary conditions. It is known that the eigenfunctions may (or may not) form a Riesz basis in the naturally associated weighted Hilbert spaces only simultaneously. Here
-
Invariant Subspaces of Idempotents on Hilbert Spaces Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-12-16 Neeru Bala, Nirupam Ghosh, Jaydeb Sarkar
In the setting of operators on Hilbert spaces, we prove that every quasinilpotent operator has a non-trivial closed invariant subspace if and only if every pair of idempotents with a quasinilpotent commutator has a non-trivial common closed invariant subspace. We also present a geometric characterization of invariant subspaces of idempotents and classify operators that are essentially idempotent.
-
Transformations of Moment Functionals Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-12-15 Philipp J. di Dio
In measure theory several results are known how measure spaces are transformed into each other. But since moment functionals are represented by a measure we investigate in this study the effects and implications of these measure transformations to moment funcationals, especially with dimensionality reduction. We gain characterizations of moment functionals. Among other things we show that for a compact
-
Realizations of Non-commutative Rational Functions Around a Matrix Centre, II: The Lost-Abbey Conditions Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-12-05 Motke Porat, Victor Vinnikov
In a previous paper the authors generalized classical results on minimal realizations of non-commutative (nc) rational functions, using nc Fornasini–Marchesini realizations which are centred at an arbitrary matrix point. In particular, it was proved that the domain of regularity of a nc rational function is contained in the invertibility set of the corresponding pencil of any minimal realization of
-
Norms of Basic Operators in Vector Valued Model Spaces and de Branges Spaces Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-11-16 Kousik Dhara, Harry Dym
Let \(\Omega _+\) be either the open unit disc or the open upper half plane or the open right half plane. In this paper, we compute the norm of the basic operator \(A_\alpha =\Pi _\Theta T_{b_\alpha }|_{\mathcal {H}(\Theta )}\) in the vector valued model space \(\mathcal {H}(\Theta )=H^m_2 \ominus \Theta H^m_2\) associated with an \(m\times m\) matrix valued inner function \(\Theta \) in \(\Omega _+\)
-
Subinner-Free Outer Factorizations on an Annulus Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-11-14 Georgios Tsikalas
-
Conjugations Preserving Toeplitz Kernels Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-10-29 Piotr Dymek, Artur Płaneta, Marek Ptak
We study conjugations in \(L^2(\mathbb {T})\) and their relation with kernels of Toeplitz operators on \(H^2(\mathbb {T})\) space. Such kernels are a generalization of model spaces. We investigate properties of an inequality relation between two unimodular functions defined on the unit circle. This allows us to significantly strengthen previous theorems characterizing all \(M_z\)-commuting and \(M_z\)-conjugations
-
A Derivative Formula for the Solid Cauchy Integral Operator and Its Applications Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-10-29 Yang Liu, Yifei Pan, Yuan Zhang
In this paper, we obtain a higher order derivative formula of the solid Cauchy integral operator on smooth bounded domains in \({\mathbb {C}}\). The formula can be used to prove a Calderón–Zygmund type theorem for higher order singular integrals, and to obtain a criterion for the solvability of the \({{\bar{\partial }}}\) problem in the flat category.
-
Weighted Cuntz–Krieger Algebras Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-10-27 Leonid Helmer, Baruch Solel
Let E be a finite directed graph with no sources or sinks and write \(X_E\) for the graph correspondence. We study the \(C^*\)-algebra \(C^*(E,Z):=\mathcal {T}(X_E,Z)/\mathcal {K}\) where \(\mathcal {T}(X_E,Z)\) is the \(C^*\)-algebra generated by weighted shifts on the Fock correspondence \(\mathcal {F}(X_E)\) given by a weight sequence \(\{Z_k\}\) of operators \(Z_k\in \mathcal {L}(X_{E^{k}})\) and
-
High-Frequency Estimates on Boundary Integral Operators for the Helmholtz Exterior Neumann Problem Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-10-17 J. Galkowski, P. Marchand, E. A. Spence
-
Reproducing Kernel Hilbert Spaces of Polyanalytic Functions of Infinite Order Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-10-07 Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini
In this paper we introduce reproducing kernel Hilbert spaces of polyanalytic functions of infinite order. First we study in details the counterpart of the Fock space and related results in this framework. In this case the kernel function is given by \(\displaystyle e^{z\overline{w}+\overline{z}w}\) which can be connected to kernels of polyanalytic Fock spaces of finite order. Segal–Bargmann and Berezin
-
Linear Combinations of Projections in Type III Factors Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-09-05 Stanisław Goldstein, Adam Paszkiewicz
It is shown that every self-adjoint operator in a \(\sigma \)-finite von Neumann factor of type III can be written as a real linear combination of 3 projections. This is in stark contrast to factors of type \(I_\infty ,\, II_1\) and \(II_\infty \), where there are always operators that require at least 4 projections in such a representation.
-
Spectral Transition for Dirac Operators with Electrostatic $$\delta $$ δ -Shell Potentials Supported on the Straight Line Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-08-30 Jussi Behrndt, Markus Holzmann, Matěj Tušek
In this note the two dimensional Dirac operator \(A_\eta \) with an electrostatic \(\delta \)-shell interaction of strength \(\eta \in {\mathbb {R}}\) supported on a straight line is studied. We observe a spectral transition in the sense that for the critical interaction strengths \(\eta =\pm 2\) the continuous spectrum of \(A_\eta \) inside the spectral gap of the free Dirac operator \(A_0\) collapses
-
Solving Continuous Time Leech Problems for Rational Operator Functions Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-08-18 A. E. Frazho, M. A. Kaashoek, F. van Schagen
The main continuous time Leech problems considered in this paper are based on stable rational finite dimensional operator-valued functions G and K. Here stable means that G and K do not have poles in the closed right half plane including infinity, and the Leech problem is to find a stable rational operator solution X such that $$\begin{aligned} G(s)X(s) = K(s) \quad (s\in \mathbb {C}_+) \quad \hbox
-
Translation-invariant Operators in Reproducing Kernel Hilbert Spaces Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-08-12 Crispin Herrera-Yañez, Egor A. Maximenko, Gerardo Ramos-Vazquez
-
Global Propagator for the Massless Dirac Operator and Spectral Asymptotics Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-08-09 Matteo Capoferri, Dmitri Vassiliev
We construct the propagator of the massless Dirac operator W on a closed Riemannian 3-manifold as the sum of two invariantly defined oscillatory integrals, global in space and in time, with distinguished complex-valued phase functions. The two oscillatory integrals—the positive and the negative propagators—correspond to positive and negative eigenvalues of W, respectively. This enables us to provide
-
Operators Which Preserve a Positive Definite Inner Product Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-07-28 Esteban Andruchow
Let \(\mathcal {H}\) be a Hilbert space, A a positive definite operator in \(\mathcal {H}\) and \(\langle f,g\rangle _A=\langle Af,g\rangle \), \(f,g\in \mathcal {H}\), the A-inner product. This paper studies the geometry of the set $$\begin{aligned} \mathcal {I}_A^a:=\{\text { adjointable isometries for } \langle \ , \ \rangle _A\}. \end{aligned}$$ It is proved that \(\mathcal {I}_A^a\) is a submanifold
-
Essential m-dissipativity for Possibly Degenerate Generators of Infinite-dimensional Diffusion Processes Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-07-21 Benedikt Eisenhuth, Martin Grothaus
First essential m-dissipativity of an infinite-dimensional Ornstein-Uhlenbeck operator N, perturbed by the gradient of a potential, on a domain \(\mathcal {F}C_b^{\infty }\) of finitely based, smooth and bounded functions, is shown. Our considerations allow unbounded diffusion operators as coefficients. We derive corresponding second order regularity estimates for solutions f of the Kolmogorov equation
-
Commutative Algebras of Toeplitz Operators on the Bergman Space Revisited: Spectral Theorem Approach Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-07-15 Grigori Rozenblum, Nikolai Vasilevski
For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the algebras of bounded functions of certain unbounded self-adjoint operators. We discuss main properties of these representation and, especially, describe relations between properties of the spectral function of Toeplitz operators
-
Backward Extensions of Weighted Shifts on Directed Trees Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-07-07 Piotr Pikul
-
On Certain Order Properties of Non Kubo–Ando Means in Operator Algebras Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-06-23 Lajos Molnár
In this paper we consider some important non Kubo–Ando means on positive definite cones of \(C^*\)-algebras and investigate their relations to the usual (Löwner) order. We study two basic questions. First, when, on the positive definite cone of a \(C^*\)-algebra, does such a mean \(\sigma \) satisfy the inequality \(A\le A \sigma B \le B\) for any pair A, B of elements with \(A\le B\). This requirement
-
Spectra for Toeplitz Operators Associated with a Constrained Subalgebra Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-05-28 Christopher Felder, Douglas T. Pfeffer, Benjamin P. Russo
A two-point algebra is a set of bounded analytic functions on the unit disk that agree at two distinct points \(a,b \in \mathbb {D}\). This algebra serves as a multiplier algebra for the family of Hardy Hilbert spaces \(H^2_t := \{ f\in H^2 : f(a)=tf(b)\}\), where \(t\in \mathbb {C}\cup \{\infty \}\). We show that various spectra of certain Toeplitz operators acting on these spaces are connected.
-
Integral Operators on Fock–Sobolev Spaces via Multipliers on Gauss–Sobolev Spaces Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-05-28 Brett D. Wick, Shengkun Wu
In this paper, we obtain an isometry between the Fock–Sobolev space and the Gauss–Sobolev space with the same order. As an application, we use multipliers on the Gauss–Sobolev space to characterize the boundedness of an integral operator on the Fock–Sobolev space.
-
The Twisted Hilbert Space Ideals Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-05-28 Félix Cabello Sánchez, Ricardo García
We study those operators on a Hilbert space that can be lifted or extended to any twisted Hilbert space. We prove that these form an ideal of operators which contains all the Schatten classes. We characterize those multiplication operators on \(\ell _p\) that are liftable/extensible through centralizers.
-
Green’s Functions for First-Order Systems of Ordinary Differential Equations without the Unique Continuation Property Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-05-28 Steven Redolfi, Rudi Weikard
This paper is a contribution to the spectral theory associated with the differential equation \(Ju'+qu=wf\) on the real interval (a, b) when J is a constant, invertible skew-Hermitian matrix and q and w are matrices whose entries are distributions of order zero with q Hermitian and w non-negative. Under these hypotheses it may not be possible to uniquely continue a solution from one point to another
-
The Agler Reducing Subspace for the Operator-Valued Inner Function Over the Bidisk Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-05-06 Senhua Zhu, Yufeng Lu, Yixin Yang
In this paper, we study the Agler reducing subspace for the compressed shift on the Beurling type quotient module \(\mathcal {K}_{\Theta }\) over the bidisk, where \(\Theta \) is an operator-valued inner function. Firstly, we characterized the Agler reducing subspace when \(\Theta \) is an one variable operator-valued inner function, which is quite different with the scalar setting. Secondly, we show
-
Power-Series Summability Methods in de Branges–Rovnyak Spaces Integr. Equ. Oper. Theory (IF 0.8) Pub Date : 2022-05-06 Javad Mashreghi, Pierre-Olivier Parisé, Thomas Ransford
We show that there exists a de Branges–Rovnyak space \({\mathcal {H}}(b)\) on the unit disk containing a function f with the following property: even though f can be approximated by polynomials in \({\mathcal {H}}(b)\), neither the Taylor partial sums of f nor their Cesàro, Abel, Borel or logarithmic means converge to f in \({\mathcal {H}}(b)\). A key tool is a new abstract result showing that, if