For a countably decomposable finite von Neumann algebra \({\mathscr {R}}\), we show that any choice of a faithful normal tracial state on \({\mathscr {R}}\) engenders the same measure topology on \({\mathscr {R}}\) in the sense of Nelson (J Funct Anal 15:103–116, 1974). Consequently it is justified to speak of ‘the’ measure topology of \({\mathscr {R}}\). Having made this observation, we extend the

In this paper, we study weighted composition–differentiation operators on the Hardy space \(H^{2}({\mathbb {D}})\). We investigate which combinations of weights \(\psi \) and maps of the open unit disk \(\varphi \) give rise to complex symmetric weighted composition–differentiation operators with conjugation \({\mathcal {C}}\), where \({\mathcal {C}}\) is a \(M_{z}\)-commuting conjugation on \(H^{2}({\mathbb

The present paper concerns the homogeneity and similarity of operators in Cowen-Douglas class \(B_n(\Omega )\). Let E be the Hermitian holomorphic vector bundle induced by \(T\in B_n(\mathbb {D})\), and \(E_{\alpha }\) be the Hermitian holomorphic vector bundle induced by \(\phi _{\alpha }(T)\), where \(\phi _{\alpha }\) is a M\(\ddot{o}\)bius transformation of the unit disk \(\mathbb {D}\). Assume

This work characterizes (dyadic homogeneous) wavelet frames for \(L^2({{\mathbb {R}}})\) by means of spectral techniques. These techniques use decomposability properties of the frame operator in spectral representations associated with the dilation operator. The approach is closely related to usual Fourier domain fiberization techniques, dual Gramian analysis, and extension principles. Spectral formulas

For an exotic locally compact Hausdorff space L, constructed under the assumption of Ostaszewski’s \(\clubsuit \)-principle, and a countable ordinal space \(\alpha \), we prove that all operators defined on \(C_0(\alpha \times L)\) have the simplest possible form. We also investigate the geometry of such space \(C_0(\alpha \times L)\) and we classify up to isomorphisms all its complemented subspaces

In this paper, we are interested in studying the set \(\mathcal {A}_{\Vert \cdot \Vert }(X, Y)\) of all norm-attaining operators T from X into Y satisfying the following: given \(\varepsilon >0\), there exists \(\eta \) such that if \(\Vert Tx\Vert > 1 - \eta \), then there is \(x_0\) such that \(\Vert x_0 - x\Vert < \varepsilon \) and T itself attains its norm at \(x_0\). We show that every norm one

Let \({\mathcal {M}}\) be a \(\sigma\)-finite von Neumann algebra, equipped with a normal faithful state \(\varphi\), and let \({\mathcal {A}}\) be maximal subdiagonal subalgebra of \({\mathcal {M}}\) and \(1\le p<\infty\). We prove a Beurling–Blecher–Labuschagne type theorem for \({{\mathcal {A}}}\)-invariant subspaces of Haagerup noncommutative \(L^p({{\mathcal {A}}})\) and give a characterization

We explore connections between boundary representations of operator spaces and those of the associated Paulsen systems. Using the notions of finite representation and separating property which we introduce for operator spaces, the boundary representations for operator spaces are characterized. We also introduce weak boundary for operator spaces. Rectangular hyperrigidity for operator spaces introduced

In this paper, we first establish the weighted compactness result for oscillation and variation associated with the truncated commutator of singular integral operators. Moreover, we establish a new \({{\mathrm{CMO}}({\mathbb {R}}^{n})}\) characterization via the compactness of oscillation and variation of commutators on weighted Lebesgue spaces.

We demonstrate how to construct spectral triples for twisted group \(C^*\)-algebras of lattices in phase space of a second-countable locally compact abelian group using a class of weights appearing in time–frequency analysis. This yields a way of constructing quantum \(C^k\)-structures on Heisenberg modules, and we show how to obtain such structures using Gabor analysis and certain weighted analogues

Let [b, T] be the commutator generated by b and T, where \(b\in \mathrm {BMO}({\mathbb {R}}^{n})\) and T is a Calderón–Zygmund singular integral operator. In this paper, the authors establish some strong type and weak type boundedness estimates including the \(L\log L\) type inequality for [b, T] on the Herz-type spaces with variable exponent. Meanwhile, the similar results for the commutators \([b

We study the generalization of m-isometries and m-contractions (for positive integers m) to what we call a-isometries and a-contractions for positive real numbers a. We show that an operator satisfying a certain inequality in hereditary form is similar to a-contraction. This improvement of [9, Theorem I] is based on some Banach algebras techniques. We show that our operator classes are closely connected

In this paper, we study continuous frames from projective representations of locally compact abelian groups of type \(\widehat{G}\times G\). In particular, using the Fourier transform on locally compact abelian groups, we obtain a characterization of maximal spanning vectors. As an application, for G, a compactly generated locally Euclidean locally compact abelian group or a local field with odd residue

Reconstruction of signals by their Fourier (transform) samples is investigated in many mathematical/engineering problems such as the inverse Radon transform and optical diffraction tomography. This paper concerns on the reconstruction of spline-spectra signals in \(V(\hbox {sinc}_{a})\) by finitely many Fourier samples, where \(\hbox {sinc}_{a}\) is the generalized sinc function. There are two main

For certain families of compact subsets of the plane, the isomorphism class of the algebra of absolutely continuous functions on a set is completely determined by the homeomorphism class of the set. This is analogous to the Gelfand–Kolmogorov theorem for C(K) spaces. In this paper, we define a family of compact sets comprising finite unions of convex curves and show that this family has the ‘Gelfand–Kolmogorov’

Let \(\mathcal {M}_{X(\mathbb {R})}\) be the Banach algebra of all Fourier multipliers on a Banach function space \(X(\mathbb {R})\) such that the Hardy–Littlewood maximal operator is bounded on \(X(\mathbb {R})\) and on its associate space \(X'(\mathbb {R})\). For two sets \(\varPsi ,\varOmega \subset \mathcal {M}_{X(\mathbb {R})}\), let \(\varPsi _\varOmega\) be the set of those \(c\in \varPsi\)

For \(i=1,2\), let \(E_i\) be a reflexive Banach lattice over \({\mathbb {R}}\) with a certain parameter \(\lambda ^+(E_i)>1\), let \(K_i\) be a locally compact (Hausdorff) topological space and let \({\mathcal {H}}_i\) be a closed subspace of \({\mathcal {C}}_0(K_i, E_i)\) such that each point of the Choquet boundary \({\text {Ch}}_{{\mathcal {H}}_i} K_i\) of \({\mathcal {H}}_i\) is a weak peak point

Current work defines Schur representation of a bilinear operator \(T: H \times H \rightarrow H\), where H is a separable Hilbert space. Introducing the concepts of self-adjoint bilinear operators, ordered eigenvalues and eigenvectors, we prove that if T is compact, self-adjoint, and its eigenvalues are ordered, then T has a Schur representation, thus obtaining a spectral theorem for T on real Hilbert

In this paper we introduce a function for multilinear operators that can be considered as an extension of the so-called outer measure associated to a linear operator ideal. We prove that it allows to characterize the operators that belong to a closed surjective ideal of multilinear operators as those having measure equal to zero. We also obtain some interpolation formulas for this new measure. As a

Let \(\varOmega \) be a proper open subset of \({\mathbb {R}}^n\) and \(p(\cdot ):\varOmega \rightarrow (0,\infty )\) a variable exponent function satisfying the globally log-Hölder continuous condition. In this article, the author introduces the variable Hardy space \(H^{p(\cdot )}(\varOmega )\) on \(\varOmega \) by the radial maximal function and then characterize the space \(H^{p(\cdot )}(\varOmega

A standard technique in infinite dimensional holomorphy, which produced several useful results, uses the Borel transform to represent linear functionals on certain spaces of multilinear operators between Banach spaces as multilinear operators. In this paper, we develop a technique to represent linear functionals, as linear operators, on spaces of multilinear operators that are beyond the scope of the

We establish a more precise description of those surjective or bijective continuous linear operators preserving orthogonality between C\(^*\)-algebras. The new description is applied to determine all uniformly continuous one-parameter semigroups of orthogonality preserving operators on an arbitrary C\(^*\)-algebra. We prove that given a family \(\{T_t: t\in {\mathbb {R}}_0^{+}\}\) of orthogonality

We consider the commutators [b, T] and \([b,I_{\rho }]\) on Orlicz-Morrey spaces, where T is a Calderón-Zygmund operator, \(I_{\rho }\) is a generalized fractional integral operator and b is a function in generalized Campanato spaces. We give a necessary and sufficient condition for the boundedness of the commutators on Orlicz-Morrey spaces. To do this we prove the boundedness of generalized fractional

In this paper, we extend the notion of orthogonality to the general elements of an absolute matrix order unit space and relate it to the orthogonality among positive elements. We introduce the notion of a partial isometry in an absolute matrix order unit space. As an application, we describe the comparison of order projections. We also discuss finiteness of order projections.

In spite of the important applications of real selfadjoint operators and monotone operators, very few papers have dealt in depth with the properties of such operators. In the present paper, we follow A. Rhodius to define the spectrum \(\sigma _{\mathbb {F}}(T)\) and the numerical range \(W_{\mathbb {F}}(T)\) of a selfadjoint operator T acting on a Hilbert space H over the real/complex field \(\mathbb

In this article, via combining Riesz norms with Morrey norms, the authors introduce and study the so-called Riesz–Morrey space, which differs from the John–Nirenberg–Campanato space in subtracting integral means. These spaces provide a bridge connecting both Lebesgue spaces and Morrey spaces which prove to be the endpoint spaces of Riesz–Morrey spaces. Moreover, the authors introduce a block-type space

We consider truncated Toeplitz operators acting on infinite dimensional model spaces. We then describe the kernels and ranks of commutators of truncated Toeplitz operators with symbols induced by certain inner functions. Our results generalize recent results of Chen et al. [Oper Matrices (to appear)] to infinite dimensional model spaces.

Dual truncated Toeplitz operators on the orthogonal complement of the model space \(K_u^2(=H^2 \ominus uH^2)\) with u nonconstant inner function are defined to be the compression of multiplication operators to the orthogonal complement of \(K_u^2\) in \(L^2\). In this paper, we give a complete characterization of the commutant of dual truncated Toeplitz operator \(D_z\), and we even obtain the commutant

This article is concerned with the random dynamics of a wide class of non-autonomous, non-local, fractional, stochastic p-Laplacian equations driven by multiplicative white noise on the entire space \({\mathbb {R}}^N\). We first establish the well-posedness of the equations when the time-dependent non-linear drift terms have polynomial growth of arbitrary orders \(p,q\ge 2\). We then prove that the

The present work either extends or improves several results on lineability of differentiable functions and derivatives enjoying certain special properties. Among many other results, we show that there exist large algebraic structures inside the following sets of special functions: (1) The class of differentiable functions with discontinuous derivative on a set of positive measure, (2) the family of

Let \(p(\cdot ):\ \mathbb {R}^n\rightarrow (0,\infty ]\) be a variable exponent function satisfying the globally log-Hölder continuous condition and A a general expansive matrix on \(\mathbb {R}^n\). Let \(H_A^{p(\cdot )}(\mathbb {R}^n)\) be the variable anisotropic Hardy space associated with A defined via the non-tangential grand maximal function. In this article, via the known atomic characterization

We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending the previous work by Langenbruch. As a consequence, we give very general conditions for these spaces to be nuclear. In particular, we obtain the corresponding results

In this paper, we define almost convex space. Let \(T:X\rightarrow Y\) be a linear bounded operator. This paper shows that: (1) If X is almost convex and 2-strictly convex, Y is a Banach space, D(T) is closed, N(T) is an approximatively compact Chebyshev subspace of D(T) and R(T) is a 2-Chebyshev hyperplane of Y, then there exists a homogeneous selection \({T^\sigma }\) of \({T^\partial }\) such that

A quantum injective frame is a frame that can be used to distinguish density operators (states) from their frame measurements, and the frame quantum detection problem asks to characterize all such frames. This problem was recently settled in Botelho-Andrade et al. (Springer Proc Math Stat 255:337–352, 2017) and Botelho-Andrade et al. (J Fourier Anal Appl 25:2268–2323, 2019) mainly for finite or infinite

The main theorem of this paper establishes a necessary and sufficient condition for embedding Schramm spaces \(\varPhi BV\) into Chanturiya classes \(V[\nu ]\). This result is new even for the classical spaces in the theory of Fourier series, namely, for the Wiener and the Salem classes. Furthermore, it provides a characterization of the embedding of Waterman classes \(\varLambda BV\) into \(V[\nu

We study pairs \((U,\mathcal{L}_0)\), where U is a unitary operator in \(\mathcal{H}\) and \(\mathcal{L}_0\subset \mathcal{H}\) is a closed subspace, such that $$\begin{aligned} P_{\mathcal{L}_0}U|_{\mathcal{L}_0}:\mathcal{L}_0\rightarrow \mathcal{L}_0 \end{aligned}$$ has a singular value decomposition. Abstract characterizations of this condition are given, as well as relations to the geometry of

Let \(\mathcal {H}\) be a right quaternionic Hilbert space and let T be a bounded quaternionic normal operator on \(\mathcal {H}\). In this article, we show that T can be factorized in a strongly irreducible sense, that is, for any \(\delta >0\) there exist a compact operator K with the norm \(\Vert K\Vert < \delta\), a partial isometry W and a strongly irreducible operator S on \(\mathcal {H}\) such

In this paper, three new algorithms are proposed for solving a pseudomonotone equilibrium problem with a Lipschitz-type condition in a 2-uniformly convex and uniformly smooth Banach space. The algorithms are constructed around the \(\phi \)-proximal mapping associated with cost bifunction. The first algorithm is designed with the prior knowledge of the Lipschitz-type constant of bifunction. This means

This paper is concerned with several important properties of weighted composition operator acting on the quaternionic Fock space \({\mathcal {F}}^2({\mathbb {H}})\). Complete equivalent characterizations for its boundedness and compactness are established. As corollaries, the descriptions for composition operator and multiplication operator on \({\mathcal {F}}^2({\mathbb {H}})\) are presented, which

In this paper, we show different inequalities for fractional-order differential operators. In particular, the Sobolev, Hardy, Gagliardo–Nirenberg, and Caffarelli–Kohn–Nirenberg-type inequalities for the Caputo, Riemann–Liouville, and Hadamard derivatives are obtained. In addition, we show some applications of these inequalities.

For a Banach space, the notion of a regular linear relation is introduced and studied. Also, the regular resolvent set for a closed linear relation is introduced and investigated. Certain characterizations of regular resolvents are obtained in terms of the gap metric between corresponding null spaces, and in terms of generalized resolvents of the linear relation itself, respectively.

In this paper, a framework of vector-valued white noise functionals has been constructed as a Gel’fand triple \({\mathcal {W}}_{\alpha }\otimes {\mathcal {E}} \subset \varGamma (H)\otimes K \subset ( {\mathcal {W}}_{\alpha }\otimes {\mathcal {E}})^*\). Base on the Gel’fand triple, a new notion of Wick product of vector-valued white noise functionals induced by a bilinear mapping \({\mathfrak {B}}:{\mathcal

In this paper the Sobolev regularity properties are investigated of the commutators of fractional maximal functions, both in the global and local case. Some new bounds for the derivatives of the above commutators will be established. As several applications, the boundedness for these operators in Sobolev spaces as well as the bounds of these operators on the Sobolev spaces with zero boundary values

A definition of relative discrete spectrum of noncommutative W*-dynamical systems is given in terms of the basic construction of von Neumann algebras, motivated from three perspectives: First, as a complementary concept to relative weak mixing of W*-dynamical systems. Second, by comparison with the classical (i.e., commutative) case. And, third, by noncommutative examples.

In previous works, an approach to the study of cyclic functions in reproducing kernel Hilbert spaces has been presented, based on the study of so called optimal polynomial approximants. In the present article, we extend such approach to the (non-Hilbert) case of spaces of analytic functions whose Taylor coefficients are in \(\ell ^p(\omega )\), for some weight \(\omega \). When \(\omega =\{(k+1)^\alpha

We study the relation of mutual strong Birkhoff–James orthogonality in two classical \(C^*\)-algebras: the \(C^*\)-algebra \({\mathbb {B}}(H)\) of all bounded linear operators on a complex Hilbert space H and the commutative, possibly nonunital, \(C^*\)-algebra. With the help of the induced graph it is shown that this relation alone can characterize right invertible elements. Moreover, in the case

Let \(M_{n}({\mathbb {R}}_{+})\) be the set of all \(n \times n\) nonnegative matrices. Recently, in Tavakolipour and Shakeri (Linear Multilinear Algebra 67, 2019, https://doi.org/10.1080/03081087.2018.1478946), the concept of the numerical range in tropical algebra was introduced and an explicit formula describing it was obtained. We study the isomorphic notion of the numerical range of nonnegative

We investigate how Fourier transform is involved in the analysis of a twisted group algebra \(L^1(G, \sigma )\) for \(G={\widehat{\Gamma }}\times \Gamma\) and \(\sigma :G\times G \rightarrow \mathbb {T}\) 2-cocycle where \(\Gamma\) is a locally compact abelian group and \({\widehat{\Gamma }}\) its Pontryagin dual related to noncommutative tori. We construct the dual Schrödinger representation which

In this paper, we study properties of weak crystal operators. In particular, we show that if \(T\in {\mathcal{L}}({\mathcal{H}})\) is a complex symmetric operator, then T is weak crystal, crystal, or crystal-like if and only if \(T^{*}\) is weak crystal, crystal, or crystal-like, respectively. Moreover, we prove that if T is a quasiaffinity, then T is weak crystal if and only if the Aluthge transform

We deal with existence and regularity for weak solutions to Dirichlet problems of the type$$\begin{aligned} \left\{ \begin{array}{ll} - \mathrm{div} (A(x)Xu) +b(x)Xu + c(x)u=f\quad \hbox {in} \; \varOmega \\ \\ u=0 \quad \quad \hbox {on} \; \partial \varOmega . \end{array} \right. \end{aligned}$$in a bounded domain \(\varOmega \) of \({\mathbb {R}}^n, n\ge 2.\) We assume that the matrix of the coefficients

In this paper we show that for an almost finite minimal ample groupoid G, its reduced \(C^*\)-algebra \(C_r^*(G)\) has real rank zero and strict comparison even though \(C_r^*(G)\) may not be nuclear in general. Moreover, if we further assume G being also second countable and non-elementary, then its Cuntz semigroup \({\mathrm{Cu}}(C_r^*(G))\) is almost divisible and \({\mathrm{Cu}}(C_r^*(G))\) and

The aim of this work is to generalize the ultraholomorphic extension theorems from V. Thilliez in the weight sequence setting and from the authors in the weight function setting (of Roumieu type) to a mixed framework. Such mixed results have already been known for ultradifferentiable classes and it seems natural that they have ultraholomorphic counterparts. In order to have control on the opening of

Let \(\theta : {\mathbb {N}}_0 \rightarrow {\mathbb {N}}_0\) be a function and \(k \in {\mathbb {N}}_0 \cup \{\infty \}\), the k-composition operator is a linear operator \(C_\theta ^k\) defined on derivative Hardy space \({\mathcal {S}}^2({\mathbb {D}})\) by \(C_\theta ^k (f) = \sum _{n=0}^k f_{\theta (n)}z^n\) for \(f(z) = \sum _{n=0}^\infty f_n z^n \text { in } {\mathcal {S}}^2({\mathbb {D}})\)

In this paper, we study the topological structure on Ext-groups of unital extensions. It is proved that the stable strong Ext-group and the stable weak Ext-group for unital extensions are pseudopolish groups if A is a unital \(C^*\)-algebra in the bootstrap class \({{\mathcal {N}}}\) and B is a stable separable \(C^*\)-algebra. Furthermore, we topologize certain UCTs and prove that these UCTs are exact

Let \({\mathcal {L}}=-\varDelta _{{\mathbb {H}}^n}+V\) be a Schrödinger operator on the Heisenberg group \({\mathbb {H}}^n\), where \(\varDelta _{{\mathbb {H}}^n}\) is the sublaplacian on \({\mathbb {H}}^n\) and the nonnegative potential V belongs to the reverse Hölder class \(RH_q\) with \(q\ge Q/2\). Here \(Q=2n+2\) is the homogeneous dimension of \({\mathbb {H}}^n\). In this paper the author first

We introduce a new class \(\mathcal {FV}(\Omega ,E)\) of weighted spaces of functions on a set \(\Omega\) with values in a locally convex Hausdorff space E which covers many classical spaces of vector-valued functions like continuous, smooth, holomorphic or harmonic functions. Then we exploit the construction of \(\mathcal {FV}(\Omega ,E)\) to derive sufficient conditions such that \(\mathcal {FV}(\Omega

Asymmetric dual truncated Toeplitz operators acting between the orthogonal complements of two (eventually different) model spaces are introduced and studied. They are shown to be equivalent after extension to paired operators on \(L^2({\mathbb {T}}) \oplus L^2({\mathbb {T}})\) and, if their symbols are invertible in \(L^\infty ({\mathbb {T}})\), to asymmetric truncated Toeplitz operators with the inverse

In the present paper, a new family of sampling type operators is introduced and studied. By the composition of the well-known generalized sampling operators of P.L. Butzer with the usual differential and anti-differential operators of order m, we obtain the so-called m-th order Kantorovich type sampling series. This family of approximation operators are very general and include, as special cases, the

This paper studies some aspects of commutant theory and functional calculus for analytic multiplication operators on Hardy and weighted Bergman spaces over bounded planar regions. Multiplication operators defined by univalent functions are shown to commute only with multiplication operators. This result is generalized to a tuple of operators, and a sufficient condition is given for irreducibility of

We completely characterize compact weighted composition operators between \(L^p\)-spaces. The relations among compactness, completely continuity, weakly compactness and M-weakly compactness of these operators are also investigated.