Generalizations of L- and M-weakly compact operators

TL;DR

This paper explores generalized forms of L- and M-weakly compact operators within Banach lattices, analyzing their regularity and algebraic properties through a unified approach involving P-operators.

Contribution

It introduces a unified framework for understanding various generalizations of L- and M-weakly compact operators using regularly P-operators.

Findings

Characterization of regularity properties of generalized operators

Identification of algebraic structures preserved under generalizations

Unified approach simplifies analysis of operator classes

Abstract

L- and M-weakly compact operators were introduced by Meyer-Nieberg in the beginning of seventies in attempts of a diversification of the concept of weakly compact operators via imposing Banach lattice structure on the range or on the domain of operators. We investigate regularity and algebraic properties of various generalizations of L- and M-weakly compact operators from a unified point of view via using regularly P-operators.