Generalized b-weakly compact operators and their factorization through KR-spaces

TL;DR

This paper explores generalized b-weakly compact operators on locally convex-solid Riesz spaces, introduces KR-spaces for their factorization, and provides new characterizations to deepen understanding of their structure and behavior.

Contribution

It introduces KR-spaces and establishes new sequential and operator characterizations for generalized b-weakly compact operators, advancing the theory in this area.

Findings

New characterizations of generalized b-weakly compact operators

Introduction of KR-spaces for operator factorization

Analogies with b-weakly compact operators through KB-spaces

Abstract

We investigate more closely the class of generalized b-weakly compact operators on locally convex-solid Riesz spaces and we provide new sequential and operator characterizations in relation with the subject. We introduce explicitly the so-called KR-spaces in order to study the factorization problem for generalized b-weakly compact operators by analogy with the well-known factorization of b-weakly compact operators through KB-spaces.