Duality and Norm Completeness in the Classes of Limitedly--Lwc and Dunford--Pettis--Lwc Operators

TL;DR

This paper explores the duality properties and norm completeness of specific classes of operators, namely limitedly--L-weakly compact and Dunford--Pettis--L-weakly compact operators, from Banach spaces to Banach lattices.

Contribution

It provides new insights into the duality and norm completeness of these operator classes, expanding the theoretical understanding in functional analysis.

Findings

Established duality properties for the operator classes.

Proved norm completeness under certain conditions.

Extended existing theory to new classes of operators.

Abstract

We investigate the duality and norm completeness in the classes of limitedly--L-weakly compact and Dunford--Pettis--L-weakly compact and operators from Banach spaces to Banach lattices.