Related papers: Generalizations of L- and M-weakly compact operato…

We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator $T$ in the weighted Lebesgue scale…

It is known that a Lipschitz continuous map from the Euclidean domain to a metric space is metrically differentiable almost everywhere. When the metric space is a Banach space dual to separable, the metric differential has its linear…

We survey recent results about composition operators induced by analytic self-maps of the unit disk in the complex plane on various Banach spaces of analytic functions taking values in infinite-dimensional Banach spaces. We mostly…

In this paper, our main purpose is to establish a weak factorization of the classical Hardy spaces in terms of a multilinear Calder\'on-Zygmund operator on the ball Banach function spaces. Furthermore, a new characterization of the BMO…

As an application of a new characterization of compactness of the $\bar\partial $-Neumann operator we derive a sufficient condition for compactness of the $\bar\partial $- Neumann operator on $(0,q)$-forms in weighted $L^2$-spaces on…

We address the problem of studying the boundedness, compactness and weak compactness of the integral operators $T_g(f)(z)=\int_0^z f(\zeta)g'(\zeta)\,d\zeta$ acting from a Banach space $X$ into $H^\infty$. We obtain a collection of general…

We show that for every weakly compact subset $K$ of $C[0,1]$ with finite Cantor-Bendixson rank, there is a reflexive Banach lattice $E$ and an operator $T:E\rightarrow C[0,1]$ such that $K\subseteq T(B_E)$. On the other hand, we exhibit an…

We investigate for a bounded semigroup of linear operators $S$ on a Banach space $E$ and a vector $x \in E$, when relative compactness of $S(I-T)x$ for every $T \in S$ implies relative compactness of the orbit $Sx$. In particular, we derive…

It has been very recently discovered that there are compact linear operators between Banach spaces which cannot be approximated by norm attaining operators. The aim of this expository paper is to give an overview of those examples and also…

Suppose $X$ is a locally solid vector lattice. It is known that there are several non-equivalent notions for compact operators on $X$. Furthermore, notion of the $AM$-property in $X$ as an extension for the $AM$-spaces in Banach lattices…

This paper considers weak supercyclicity for bounded linear operators on a normed space. On the one hand, weak supercyclicity is investigated for classes of Hilbert-space operators: (i) self-adjoint operators are not weakly supercyclic,…

For an operator T from X to Y denote m(T) the infimum of $||Tx||$ on the unit sphere $S_X$ of X. A sequence $(x_n)$ in $S_X$ is said to be minimizing for T if $||Tx_n||$ tends to m(T). In 2020 U. S. Chakraborty introduced and studied the…

Recently, the functionals different types of unbounded convergences (uo, un, uaw, uaw*) in Banach lattices were studied. In this paper, we study the continuous operators with respect to unbounded convergences. We first investigate the…

We describe the spectrum of weighted $d$-isomorphisms of Banach lattices restricted on closed subspaces that are "rich" enough to preserve some "memory" of the order structure of the original lattice. The examples include (but are not…

We provide explicit examples of positive and power-bounded operators on $c_0$ and $\ell^\infty$ which are mean ergodic but not weakly almost periodic. As a consequence we prove that a countably order complete Banach lattice on which every…

As generalizations of skew left braces, weak left braces were introduced recently by Catino, Mazzotta, Miccoli and Stefanelli to study ceratin special degenerate set-theoretical solutions of the Yang-Baxter equation. In this note, as…

A classification of weakly compact multiplication operators on L(L_p), $1<p<\infty$, is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of $\ell_p$-strictly singular operators, and…

In this paper, we introduce the concept of the m-generalized right group inverse. This serves as a natural extension of both the m-weak group inverse and the generalized group inverse. We characterize this new generalized inverse using the…

The notion of $\mathcal{O}$-operators on modules over Lie algebras generalize Rota-Baxter operators. They also generalize Poisson structures on Lie algebras in the presence of modules. Motivated from Poisson structures, we define gauge…

For operators representing ill-posed problems, an ordering by ill-posedness is proposed, where one operator is considered more ill-posed than another one if the former can be expressed as a cocatenation of bounded operators involving the…