Unbounded $M$-weakly and unbounded $L$-weakly compact operators

TL;DR

This paper introduces and studies unbounded versions of $M$-weakly and $L$-weakly compact operators, exploring their properties, relationships, and characterizations within Banach lattices.

Contribution

It defines unbounded $M$-weakly and $L$-weakly compact operators and investigates their properties and relations to existing operator classes, including a characterization of Banach lattices.

Findings

Unbounded $M$-weakly and $L$-weakly compact operators are introduced.

Relationships between unbounded and classical weakly compact operators are established.

Characterization of Banach lattices with order continuous norm is provided.

Abstract

We introduce the class of unbounded $M$-weakly operators and the class of unbounded $L$-weakly compact operators. We investigate some properties for these new classification of operators and we study relation between them and $M$-weakly compact and $L$-weakly compact operators. We also present an operator characterization of Banach lattices with order continuous norm. \keywords{unbounded $M$-weakly compact \and unbounded $L$-weakly compact \and unbounded norm convergence \and $M$-weakly compact \and $L$-weakly compact