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

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

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.

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 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

We study, among others, upper, lower, upper modified and lower modified n-th von Neumann–Jordan constant and relationships between them. There are characterized uniformly non-\(l_{n}^{1}\) Banach spaces in terms of the upper modified n-th von Neumann–Jordan constant. Moreover, this constant is calculated explicitly for Lebesgue spaces \(L^{p}\) and \(l^{p}\)\((1\le p\le \infty ).\) Finally, it is shown

Let \(\mathbb {Y}\) be either an Orlicz sequence space or a Marcinkiewicz sequence space. We take advantage of the recent advances in the theory of factorization of the identity carried on by Lechner (Stud Math 248(3):295–319, 2019) to provide conditions on \(\mathbb {Y}\) that ensure that, for any \(1\le p\le \infty \), the infinite direct sum of \(\mathbb {Y}\) in the sense of \(\ell _p\) is a primary

The properties of the class of functions of generalized bounded variation are studied. The “anomaly” feature of this class is revealed. There is the notation of absolute continuity with respect to \(((p_n), \phi )\) and it’s connection with the ordinary absolute continuity is investigated. The problems of approximation by Steklov’s functions and singular integrals are studied.

The mixed Lebesgue space is a suitable tool for modeling and measuring signals living in time-space domains. And sampling in such spaces plays an important role for processing high-dimensional time-varying signals. In this paper, we first define reproducing kernel subspaces of mixed Lebesgue spaces. Then, we study the frame properties and show that the reproducing kernel subspace has finite rate of

We study the structural and linear topological properties of the space \(\dot{\mathcal {B}}^{\prime *}_{\omega }\) of ultradistributions vanishing at infinity (with respect to a weight function \(\omega \)). Particularly, we show the first structure theorem for \(\dot{\mathcal {B}}^{\prime *}_{\omega }\) under weaker hypotheses than were known so far. As an application, we determine the structure of

The equation \(\bigl (Fu'\bigr )(t)=\bigl (Gu\bigr )(t)+f(t)\), \(t\in {\mathbb {R}}\), where F and G are bounded linear operators, is considered. It is assumed that infinity is a pole of the resolvent of the pencil \(\lambda \mapsto \lambda F-G\) and the spectrum of the pencil is disjoint from the imaginary axis. Under these assumptions, to each free term f bounded on \({\mathbb {R}}\) (in the sense

In this paper, we characterize the mapping properties of Hankel operators \(H_{g}\) and \( H_{\overline{g}}\) associated to some restricted function g on the complex space \(\mathbf{C}^n\). We, in particular, describe the boundedness and compactness of operators \(H_{g}\) and \( H_{\overline{g}}\) acting between Fock spaces in terms of Berezin transforms of their inducing function g. Our results extend

We study non-linear functionals, including quasi-linear functionals, p-conic quasi-linear functionals, d-functionals, r-functionals, and their relationships to deficient topological measures and topological measures on locally compact spaces. We prove representation theorems and show, in particular, that there is an order-preserving, conic-linear bijection between the class of finite deficient topological

Various fundamental formulas and results for integral transforms on a function space have been studied in many papers. However, there are many limitations with regard to obtaining the fundamental formulas and results with respect to integral transforms on the function space, because generalized Brownian motion has the nonzero mean function. Despite recent attempts address this problem, it has yet to

In this paper, we prove that if \(T\in {\mathcal {L}({\mathcal {H}})}\) is complex symmetric, then its generalized mean transform \({\widehat{T}}(t)~ (t\not =0)\) of T is also complex symmetric. Next, we consider complex symmetry property of the mean transform \({\widehat{T}}(0)\) of truncated weighted shift operators. Finally, we study properties of the generalized mean transform of skew complex symmetric