Related papers: Regular matrices of unbounded linear operators

Let ${\mathcal B}$ be a Banach algebra and ${\mathcal A}$ be a Banach subalgebra that admits norm-controlled inversion in ${\mathcal B}$. In this work, we take $A, B$ in the Banach subalgebra ${\mathcal A}$ with their spectra in the Banach…

A recent result of Leung (Proceedings of the American Mathematical Society, to appear) states that the Banach algebra $\mathscr{B}(X)$ of bounded, linear operators on the Banach space…

A proof is given for the "only if" part of the result stated in the previous paper of the series that a suitably nondegenerate Calder\'on-Zygmund operator $T$ is bounded in a Banach lattice $X$ on $\mathbb R^n$ if and only if the…

In this paper we completely characterize the norm attainment set of a bounded linear operator on a Hilbert space. This partially answers a question raised recently in [\textit{D. Sain, On the norm attainment set of a bounded linear…

We characterize classes of linear maps between operator spaces $E$, $F$ which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative $L^p$ spaces $S_p[E^*]$ based on the Schatten classes on the…

For $X$ an infinite dimensional Banach space, we contribute to the study of the Banach algebra $L(X)/S(X)$, where $S(X)$ is the ideal of strictly singular operators. We extend results of Ferenczi-Galego (2007) by proving that $\|I-J\|_S…

We investigate two systematic constructions of inverse-closed subalgebras of a given Banach algebra or operator algebra A, both of which are inspired by classical principles of approximation theory. The first construction requires a closed…

We consider a family of norms (called operator E-norms) on the algebra $B(H)$ of all bounded operators on a separable Hilbert space $H$ induced by a positive densely defined operator $G$ on $H$. Each norm of this family produces the same…

Given a Banach lattice $L,$ the space of lattice Lipschitz operators on $L$ has been introduced as a natural Lipschitz generalization of the linear notions of diagonal operator and multiplication operator on Banach function lattices. It is…

We exhibit an operator norm bounded, infinite sequence $\{A_n\}$ of $3n \times 3n$ complex matrices for which the commutator map $X\mapsto XA_n - A_nX$ is uniformly bounded below as an operator over the space of trace-zero self-adjoint…

A full description of the membership in the Schatten ideal $S_ p(A^2_{\omega})$ for $0<p<\infty$ of the Toeplitz operator acting on large weighted Bergman spaces is obtained.

Let $\bold{\Phi}=(\phi_n)$ be a Musielak-Orlicz function, $X$ be a real Banach space and $A$ be any infinite matrix. In this paper, a generalized vector-valued Musielak-Orlicz sequence space $l_{\bold {\Phi}}^{A}(X)$ is introduced. It is…

Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…

Let A be a unital standard algebra on a complex Banach space X with dimX >1. We characterize the linear maps D; T : A --> B(X) satisfying aT(b) + D(a)b= 0 whenever a,b in A are such that ab = 0.

This paper studies Rota-Baxter operators on the matrix $C^*$-algebra $M_n(\mathbb{C})$, motivated by the discrete Toeplitz algebra (whose role is purely heuristic; see Remark~\ref{rem:toeplitz_scope}). We provide a structural classification…

We study the lattice of closed ideals of bounded operators on two families of Banach spaces: the Baernstein spaces $B_p$ for $1<p<\infty$ and the Schreier spaces $S_p$ for $1\le p<\infty$. Our main conclusion is that there are…

Let $X$ be a Banach function space over the unit circle such that the Riesz projection $P$ is bounded on $X$ and let $H[X]$ be the abstract Hardy space built upon $X$. We show that the essential norm of the Toeplitz operator $T(a):H[X]\to…

Let $\mathbb{B}(\mathcal{H})$ denote the $C^{\ast}$-algebra of all bounded linear operators on a Hilbert space $\big(\mathcal{H}, \langle\cdot, \cdot\rangle\big)$. Given a positive operator $A\in\B(\h)$, and a number $\lambda\in [0,1]$, a…

In the framework of operator theory, we investigate a close Lie theoretic relationship between all operator ideals and certain classical groups of invertible operators that can be described as the solution sets of certain algebraic…

This paper is a follow-up to the paper [Matrix periods and competition periods of Boolean Toeplitz matrices, {\it Linear Algebra Appl.} 672:228--250, (2023)]. Given subsets $S$ and $T$ of $\{1,\ldots,n-1\}$, an $n\times n$ Toeplitz matrix…