Related papers: Limitedly L-weakly compact operators

We introduce and study the class of positive weakly (q,r)-dominated multilinear operators between Banach lattices. This notion extends classical domination and summability concepts to the positive multilinear setting and generates a new…

The aim of this article is to extend results of Maslyuchenko O., Mykhaylyuk V. Popov M. about narrow operators on vector lattices. We give a new definition of a narrow operator where a vector lattice as the domain space of a narrow operator…

V. D. Milman proved in \cite{Milman:70} that the product of two strictly singular operators on $L_p[0,1]$ ($1\le p<\infty$) or on $C[0,1]$ is compact. In this note we utilize Schreier families $\S_\xi$ in order to define the class of…

We introduce and study some operational quantities which characterize the disjointly non-singular operators from a Banach lattice $E$ to a Banach space $Y$ when $E$ is order continuous, and some other quantities which characterize the…

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…

We introduce the notions of tauberian, cotauberian and weakly compact pair of closed subspaces of a Banach space. The theory produced by these notions is richer than that of the corresponding operators since an operator can be regarded as a…

Let $K$ be an absolutely convex infinite-dimensional compact in a Banach space $\mathcal{X}$. The set of all bounded linear operators $T$ on $\mathcal{X}$ satisfying $TK\supset K$ is denoted by $G(K)$. Our starting point is the study of the…

We introduce the class of Orlicz-Pettis polynomials between Banach spaces, defined by their action on weakly unconditionally Cauchy series. We give a number of equivalent definitions, examples and counterexamples which highlight the…

We construct a slightly new noncommutative Calder\'on-Zygmund decomposition by further splitting the bad function. Using this tool, we prove the weak type (1,1) boundedness of noncommutative Calder\'on-Zygmund operators under a class of…

In this work we provide a characterization of distinct type of (linear and non-linear) maps between Banach spaces in terms of the differentiability of certain class of Lipschitz functions. Our results are stated in an abstract bornological…

Denote by $[0,\omega_1)$ the locally compact Hausdorff space consisting of all countable ordinals, equipped with the order topology, and let $C_0[0,\omega_1)$ be the Banach space of scalar-valued, continuous functions which are defined on…

We characrterize extreme contractions defined between \ finite-dimensional polyhedral Banach spaces using $k$- smoothness of operators. We also explore weak L-P property, a recently introduced concept in the study of extreme contractions.…

A bounded linear operator between Banach spaces is called {\it completely continuous} if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class of non-completely-continuous…

We establish the weak Banach-Saks property for function spaces arising as the optimal domain of an operator.

This paper provides conditions (i) to distinguish weak supercyclicity form supercyclicity for operators acting on normed and Banach spaces, and also (ii) to ensure when weak supercyclicity implies weak stability.

To appear in J. Funct. Spaces and Appl.

In this paper, we study $un$-dual (in symbol, $\ud{E}$) of Banach lattice $E$ and compare it with topological dual $E^*$. If $E^*$ has order continuous norm, then $E^* = \ud{E}$. We introduce and study weakly unbounded norm topology…

An algebra of bounded linear operators on a Banach space is said to be {\em strongly compact} if its unit ball is precompact in the strong operator topology, and a bounded linear operator on a Banach space is said to be {\em strongly…

We discuss compactness of the d-bar-Neumann operator in the setting of weighted L^2-spaces on C^n.$ For this purpose we use a description of relatively compact subsets of L^2- spaces. We also point out how to use this method to show that…

This paper presents a new formulation of the fractional Laplacian operator $(-\Delta)^s$ in $n$-dimensional space ($n \ge 1$). The proposed formulation expresses $(-\Delta)^s$ as a composition of the classical Laplace differential operator…