Order almost DUNFORD-PETTIS Operators on Banach lattices

TL;DR

This paper introduces and studies order almost Dunford-Pettis operators in Banach lattices, exploring their properties and characterizations related to well-known operator classes.

Contribution

It defines new classes of operators in Banach lattices and characterizes Banach lattices where these operators coincide with almost weakly limited operators.

Findings

Properties of order almost Dunford-Pettis operators established.

Characterizations of Banach lattices where these operators are almost weakly limited.

Connections made with existing classes like order weakly compact and Dunford-Pettis operators.

Abstract

By introducing the concepts of order almost Dunford-Pettis and almost weakly limited operators in Banach lattices, we give some properties of them related to some well known classes of operators, such as, order weakly compact, order Dunford-Pettis, weak and almost Dunford-Pettis and weakly limited operators. Then, we characterize Banach lattices E and F on which each operator from E into F that is order almost Dunford-Pettis and weak almost Dunford-Pettis is an almost weakly limited operator.