Demi Weakly Dunford-Pettis on Banach Spaces

TL;DR

This paper introduces and explores weakly Demi Dunford-Pettis operators in Banach spaces, examining their properties, relationships with other operator classes, and behavior within Banach lattices.

Contribution

It defines the new class of weakly Demi Dunford-Pettis operators and analyzes their connections with existing operator classes and their behavior in Banach lattices.

Findings

Characterization of weakly Demi Dunford-Pettis operators

Conditions under which these operators coincide with Demi Dunford-Pettis and Demicompacts

Behavior of these operators in Banach lattice environments

Abstract

In this paper, our main goal is to define the class of weakly Demi Dunford-Pettis applications. We also study their relationship with the classes of weakly Dunford-Pettis and Demi Dunford-Pettis operators, including a condition where these operators coincide with Demi Dunford-Pettis and Demicompacts. In the last section, we study some of the behavior of this class in the Banach Lattice environment.