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.

In this paper we express the eigenvalues of anti-heptadiagonal persymmetric Hankel matrices as the zeros of explicit polynomials giving also a representation of its eigenvectors. We present also an expression depending on localizable parameters to compute its integer powers. In particular, an explicit formula not depending on any unknown parameter for the inverse of anti-heptadiagonal persymmetric

The main purpose of this paper is to establish a Hardy space theory associated with a new multi-parameter structure and characterize this Hardy space as the intersection of flag Hardy spaces. The key idea used here is to identify the new kernels as sums of two flag kernels.

We introduce and study modular Birkhoff–James orthogonality for typical Banach modules \(B({\mathbb {X}},{\mathbb {Y}})\) and \(K({\mathbb {X}},{\mathbb {Y}}),\) where \({\mathbb {X}}\) and \({\mathbb {Y}}\) are Banach spaces. We present some basic characterizations of modular Birkhoff–James orthogonality under certain restrictions, and completely characterize left symmetric points for the said orthogonality

In this paper, we introduce the concept of a strongly asymptotically quasi-nonexpansive sequence of mappings in the context of a Hilbert space. Firstly, we prove the weak convergence of a Picard type iterative method to a common fixed point for the sequence as well as the strong convergence when a Halpern type regularization scheme is considered. Among other features, our results are applied to get

Let \({\mathcal {M}}\) be a diffuse von Neumann algebra equipped with a fixed faithful, normal, semi-finite trace and let \(\varphi\) be an Orlicz function. In this paper, a new approach to the noncommutative Yosida–Hewitt decomposition in noncommutative Calderón–Lozanovskiĭ spaces \(E_\varphi ({\mathcal {M}})\) is presented. It is a new result even in the commutative case. In the meanwhile, the related

In this paper we generalize the concept of Davis–Wielandt shell of operators on a Hilbert space when a semi-inner product induced by a positive operator A is considered. Moreover, we investigate the parallelism of A-bounded operators with respect to the seminorm and the numerical radius induced by A. Mainly, we characterize A-normaloid operators in terms of their A-Davis–Wielandt radii. In addition

We introduce and study the Lipschitz injective hull of Lipschitz operator ideals defined between metric spaces. We show some properties and apply the results to the ideal of Lipschitz p-nuclear operators, obtaining the ideal of Lipschitz quasi p-nuclear operators. Also, we introduce in a natural way the ideal of Lipschitz Pietsch p-integral operators and show that its Lipschitz injective hull coincide

A non compactness measure with values in the lattice of extended non negative real numbers \([0, +\infty ]\) is introduced in the general setting of a Hausdorff topological vector space E. This generalizes the classical Kuratowski and Hausdorff non compactness measures. In order to achieve this, we introduce the notions of basic and sufficient collections of zero neighborhoods. We then show that our

We study the well-posedness of the third order degenerate differential equations with infinite delay$$(P_3): (Mu)'''(t) + (Lu)''(t) + (Bu)'(t)= Au(t) + \int _{-\infty }^t a(t-s)Au(s)ds + f(t){\text{ on }}[0, 2\pi ]$$in Lebesgue–Bochner spaces \(L^p(\mathbb{T};\; X)\) and periodic Besov spaces \(B_{p,\,q}^s(\mathbb{T};\; X)\), where A, B, L and M are closed linear operators on a Banach space X satisfying

The purpose of this paper is to provide a set of sufficient conditions so that the normalized form of the Fox–Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit disc. In particular, we study some geometric properties for some class of functions related to the generalized hypergeometric functions.

An important problem stemming from perturbation theory concerns description and understanding of operator \(\theta \)-Hölder functions. This article presents a survey of recent developments concerning operator \(\theta \)-Hölder functions with respect to symmetric quasi-norms.

Let \(L_M\) be an Orlicz function space endowed with the Orlicz norm or the Luxemburg norm, and let X be a Banach space. In this paper we characterize the non-\(l_n^{(1)}\) point and the uniformly non-\(l_{n}^{(1)}\) point of Orlicz–Bochner function space \(L_M(\mu ,X)\). As the immediate consequences some criteria for non-square point and uniformly non-square point of \(L_M(\mu ,X)\) are obtained

In this manuscript, we transport the classical Operator Theory on complex Banach spaces to normed modules over absolutely valued rings. In some cases, we are able to extend classical results on complex Banach spaces to normed modules over normed rings. In order to make sure that bounded linear maps on normed modules coincide with the continuous linear maps, it is sufficient that the underlying ring

Let \({{\mathscr {M}}}\) be a \(II_1\) factor acting on the Hilbert space \({{\mathscr {H}}}\), and \({\mathscr {M}} _{\text {aff}}\) be the Murray–von Neumann algebra of closed densely-defined operators affiliated with \({{\mathscr {M}}}\). Let \(\tau \) denote the unique faithful normal tracial state on \(\mathscr {M}\). By virtue of Nelson’s theory of non-commutative integration, \({\mathscr {M}}

We analyze f-frequently hypercyclic, q-frequently hypercyclic (\(q> 1\)), and frequently hypercyclic \(C_{0}\)-semigroups (\(q=1\)) defined on complex sectors,with values in separable infinite-dimensional Fréchet spaces. Some structural results are given for a general class of \({\mathcal F}\)-frequently hypercyclic \(C_{0}\)-semigroups, as well. We investigate generalized frequently hypercyclic translation

We establish weighted extrapolation theorems in classical and grand Lorentz spaces. As a consequence we have the weighted boundedness of operators of Harmonic Analysis in grand Lorentz spaces. We treat both cases: diagonal and off-diagonal ones.

We consider subspaces of Morrey spaces defined in terms of various vanishing properties of functions. Such subspaces were recently used to describe the closure of \(C_0^\infty ({\mathbb {R}^n})\) in Morrey norm. We show that these subspaces are invariant with respect to some classical operators of harmonic analysis, such as the Hardy–Littlewood maximal operator, singular type operators and Hardy operators

A generalization of the products of composition, multiplication and differentiation operators is the Stević–Sharma operator \(T_{u_1,u_2,\varphi }\), defined by \(T_{u_1,u_2,\varphi }f=u_1\cdot f\circ \varphi +u_2\cdot f'\circ \varphi \), where \(u_1,u_2,\varphi \) are holomorphic functions on the unit disk \({\mathbb {D}}\) in the complex plane \({\mathbb {C}}\) and \(\varphi ({\mathbb {D}})\subset

We study Birkhoff-James orthogonality and isosceles orthogonality of bounded linear operators between Hilbert spaces and Banach spaces. We explore Birkhoff-James orthogonality of bounded linear operators in light of a new notion introduced by us and also discuss some of the possible applications in this regard. We also study isosceles orthogonality of bounded (positive) linear operators on a Hilbert

In this work, we present new existence results for a system of quadratic integral equations of Fredholm type on the whole space \({\mathbb {R}}^n\). By using a technique based on a fixed point theorem expressed in terms of some measures of noncompactness, we generalize existence results obtained in both Aghajani and Haghighi (Novi Sad J Math 44.1:59–73, 2014) and Arab (Filomat 30(11):3063–3073, 2016)

In this article, the authors consider the Schrödinger type operator \(L:=-\mathrm{div}(A\nabla )+V\) on \({\mathbb {R}}^n\) with \(n\ge 3\), where the matrix A satisfies uniformly elliptic condition and the nonnegative potential V belongs to the reverse Hölder class \(RH_q({\mathbb {R}}^n)\) with \(q\in (n/2,\,\infty )\). Let \(p(\cdot ):\ {\mathbb {R}}^n\rightarrow (0,\,\infty )\) be a variable exponent

We introduce the notions of kernel map and kernel set of a bounded linear operator on a Hilbert space relative to a subspace lattice. The characterization of the kernel maps and kernel sets of finite rank operators leads to showing that every norm closed Lie module of a continuous nest algebra is decomposable. The continuity of the nest cannot be lifted, in general.

In this paper we establish the subelliptic Picone type identities. As consequences, we obtain Hardy and Rellich type inequalities for anisotropic p-sub-Laplacians which are operators of the form$$\begin{aligned} {\mathcal {L}}_{p}f:= \sum _{i=1}^{N} X_i\left( |X_i f|^{p_i-2} X_i f \right) ,\quad 1

We define and characterize the core inverse in the context of Banach algebras. The Banach space operator case is also considered. Using the core inverse, we present new characterizations of EP Banach space operators and EP Banach algebra elements. The dual core inverse for Banach algebra elements is presented too. Some new characterizations of co–EP Banach algebra elements are given by means the core

Let \(\mathcal {H}\) be a separable Hilbert space and P be an idempotent on \(\mathcal {H}.\) We set$$\begin{aligned} \Gamma _{P}=\left\{ J: J=J^{*}=J^{-1} \quad \hbox { and }\quad JPJ=I-P\right\} \end{aligned}$$and$$\begin{aligned} \Delta _{P}=\left\{ J: J=J^{*}=J^{-1} \quad \hbox { and }\quad JPJ=I-P^*\right\} . \end{aligned}$$In this paper, we first get that symmetries \((2P-I)|2P-I|^{-1}\) and

The Darboux-like functions represent a group of maps that are continuous in a generalized sense. The algebra of subsets of \({\mathbb {R}}^{\mathbb {R}}\) (i.e., maps from \({\mathbb {R}}\) to \({\mathbb {R}}\)) generated by these classes has nine atoms, that is, the smallest non-empty elements of the algebra. The subject of this work is to study the intersections of these atoms with the class \({{\

The concept of R-duals of a sequence was first introduced with the motivation to obtain a general version of duality principle in Gabor analysis. Since then, various R-duals (types II, III, IV) and some relaxations of the R-dual setup have been introduced and studied by some mathematicians. All these “R-duals” provide a powerful tool in the analysis of duality relations in general frame theory. It

Let \({\mathcal {B}}\) be a class of finite-dimensional Banach spaces. A \({\mathcal {B}}\)-decomposed Banach space is a Banach space X endowed with a family \({\mathcal {B}}_X\subset {\mathcal {B}}\) of subspaces of X such that each \(x\in X\) can be uniquely written as the sum of an unconditionally convergent series \(\sum _{B\in {\mathcal {B}}_X}x_B\) for some \((x_B)_{B\in {\mathcal {B}}_X}\in

We give the existence theorem of piecewise weighted pseudo almost periodic mild solutions for impulsive integro-differential equations with fractional order \(1<\alpha <2\), where A is a linear closed and densely defined operator of sectorial type in a complex Banach space \({{\mathbb {X}}}\). The main results are obtained by Banach contraction mapping principle. An example is given to illustrate the

Park and Skoug established several integration by parts formulas involving analytic Feynman integrals, analytic Fourier–Feynman transforms, and the first variation of cylinder-type functionals of standard Brownian motion paths in Wiener space \(C_0[0,T]\). In this paper, using a very general Cameron–Storvick theorem on the Wiener space \(C_0[0,T]\), we establish various integration by parts formulas

For \(C^*\)-algebras A and B, we show that there is a natural homeomorphism from the product of spaces of maximal (resp., maximal modular) ideals of A and B onto the space of maximal (resp., maximal modular) ideals of \(A \otimes ^\gamma B\), with respect to the hull-kernel topology. This is based on and preceded by an analysis of the structure of closed ideals of \(A \otimes ^\gamma B\) in terms of