Limitedly L-weakly compact operators

TL;DR

This paper introduces a new class of limitedly L-weakly compact operators in Banach spaces, providing characterizations, exploring domination, and analyzing their completeness, thus extending the hierarchy of compact operators.

Contribution

The paper defines a novel class of operators, compares it with existing classes, and investigates its properties and structure within Banach spaces.

Findings

The new class properly contains L-weakly compact operators.

Characterization of the class via sequences is provided.

The class's completeness is studied.

Abstract

We introduce new class of limitedly L-weakly compact operators from a Banach space to a Banach lattice. This class is a proper subclass of the Bourgain-Diestel operators and it contains properly the class of L-weakly compact operators. We give its efficient characterization in term of sequences, investigate the domination problem, and study the completeness of this class of operators.