Contribution to operators between Banach lattices

TL;DR

This paper introduces a new class of operators on Banach lattices that unify several classical operator classes and explores their lattice approximation properties.

Contribution

It defines a novel class of operators on Banach lattices that generalizes multiple existing classes and investigates their approximation properties.

Findings

Unified several classical operator classes under a new framework

Established new lattice approximation properties for these operators

Provided insights into the structure of operators on Banach lattices

Abstract

In this paper we introduce and study a new class of operators related to norm bounded sets on Banach Lattice and which brings together several classical classes of operators (as o-weakly compact operators, b-weakly compact operators, M-weakly compact operators, L-weakly compact operators, almost Dunford-Pettis operators). As consequences, we give some new lattice approximation properties of these classes of operators.