Related papers: Two-sided multiplication operators on the space of…

Let $X$ be a Borel metric measure space such that each closed ball is of positive and finite measure. In this paper, we give a sufficient and necessary condition for averaging operators on a Banach function space $E(X)$ on $X$ to be…

We study octahedral norms in the space of bounded linear operators between Banach spaces. In fact, we prove that $L(X,Y)$ has octahedral norm whenever $X^*$ and $Y$ have octahedral norm. As a consequence the space of operators $L(\ell_1…

An extension of Marcinkiewicz Interpolation Theorem, allowing intermediate spaces of Orlicz type, is proved. This generalization yields a necessary and sufficient condition so that every quasilinear operator, which maps the set, $S(X,\mu)$,…

Let $E$ be a complex Banach lattice and $T$ is an operator in the centrum $Z(E)=\{T: |T|\le \lambda I \mbox{ for some } \lambda\}$ of $E$. Then the essential norm $\|T\|_{e}$ of $T$ equals the essential spectral radius $r_{e}(T)$ of $T$. We…

Let $X$, $Y$, and $Z$ be Banach spaces, and let $\alpha$ be a tensor norm. Let a bounded linear operator $S\in\mathcal{L}(Z,\mathcal{L}(X,Y))$ be given. We obtain (necessary and/or sufficient) conditions for the existence of an operator…

Let $\mu$ be a non-negative Radon measure on ${\mathbb R}^d$ which only satisfies the polynomial growth condition. Let ${\mathcal Y}$ be a Banach space and $H^1(\mu)$ the Hardy space of Tolsa. In this paper, the authors prove that a linear…

It follows, from a generalised version of Paley-Wiener theorem, that the Laplace transform is an isometry between certain spaces of weighted $L^2$ functions defined on $(0, \infty)$ and (Hilbert) spaces of analytic functions on the right…

We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke)…

The purpose of this survey article is a comprehensive study of operator Lipschitz functions. A continuous function $f$ on the real line ${\Bbb R}$ is called operator Lipschitz if $\|f(A)-f(B)\|\le{\rm const}\|A-B\|$ for arbitrary…

Let $\mathbb{X}$ be a Banach space and let $\mathbb{X}^*$ be the dual space of $\mathbb{X}.$ For $x,y \in \mathbb{X},$ $ x$ is said to be $T$-orthogonal to $y$ if $Tx(y) =0,$ where $T$ is a bounded linear operator from $\mathbb{X}$ to…

In this paper, we investigate operators on Riesz algebras, which are continuous with respect to multiplicative modifications of order convergence and relatively uniform convergence. We also introduce and study mo-Lebesgue, mo-$KB$, and…

We investigate expansive Hilbert space operators $T$ that are finite rank perturbations of isometric operators. If the spectrum of $T$ is contained in the closed unit disc $\overline{\mathbb{D}}$, then such operators are of the form $T=…

We show that every complemented modular lattice can be converted into a left residuated lattice where the binary operations of multiplication and residuum are term operations. The concept of an operator left residuated poset was introduced…

The purpose of the paper is to study the operators on the weighted Bergman spaces on the unit disk ${\mathbb{D}}$, denoted by $A^{p}_{\lambda,w}({\mathbb{D}})$, that are associated with a class of generalized analytic functions, named the…

For an operator $T \in B(X,Y)$, we denote by $a_m(T)$, $c_m(T)$, $d_m(T)$, and $t_m(T)$ its approximation, Gelfand, Kolmogorov, and absolute numbers. We show that, for any infinite dimensional Banach spaces $X$ and $Y$, and any sequence…

We introduce and characterize, on the Banach lattice valued continuous function space, multiplication operators generating strongly continuous multiplication operator semigroups. Our characterization is the generalization of known results…

Researchers have identified complex matrices $A$ such that a bounded linear operator $B$ acting on a Hilbert space will admit a dilation of the form $A \otimes I$ whenever the numerical range inclusion relation $W(B) \subseteq W(A)$ holds.…

We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform.

We prove an abstract theorem on keeping the compactness property of a linear operator after interpolation in Banach spaces. No analytical presentation of operators, spaces and interpolation functor is required. We use only some little-known…

We give new necessary and sufficient conditions for the numerical range $W(T)$ of an operator $T \in \mathcal{B}(\mathcal{H})$ to be a subset of the closed elliptical set $K_\delta \subseteq \mathbb{C}$ given by \[ K_\delta {\stackrel{\rm…