On the disjoint weak Banach-Saks operators

TL;DR

This paper introduces disjoint weak Banach-Saks operators, characterizes them through various convergence types, and explores their relationships with other operator classes, providing new insights into their properties.

Contribution

It presents the first comprehensive study and characterizations of disjoint weak Banach-Saks operators using different convergence notions and positive weakly null sequences.

Findings

Characterization via multiple convergence types

New description of the disjoint weak Banach-Saks property

Relationships with other operator classes

Abstract

We introduce and study a new class of operators that we call disjoint weak Banach-Saks operators. We establish some characterizations of this class of operators by different types of convergence (norm convergence, unbounded order convergence, unbounded norm convergence and unbounded absolute weak convergence) as well as by the positive weakly null sequences. Consequently, we give a new characterization of the disjoint weak Banach-Saks property by the positive disjoint weakly null sequences. Furthermore, we study the relationship between this class and other classes of operators.