On collectively L-weakly compact sets of operators

TL;DR

This paper explores the properties of collectively L-weakly compact sets of operators between Banach spaces and lattices, extending duality theorems and analyzing their relations to other compactness concepts.

Contribution

It extends Meyer-Nieberg duality to collectively L-weakly compact operators and investigates their connections with almost limited sets and domination problems.

Findings

Extended Meyer-Nieberg duality theorem to these sets

Established relations with collectively almost limited sets

Discussed domination problems for these operator sets

Abstract

A set of bounded linear operators from a Banach space to a Banach lattice is collectively L-weakly compact whenever union of images of the unit ball is L-weakly compact. We extend the Meyer-Nieberg duality theorem to collectively L-weakly compact sets of operators, study relations between these sets and collectively almost limited sets, and discuss the domination problem for collectively compact sets and collectively L-weakly compact sets.