Representation of Compact Operators between Banach spaces

TL;DR

This paper provides a generalized representation for compact operators between reflexive Banach spaces, extending previous results and including operators comparable to compact normal operators on Hilbert spaces, with illustrative examples.

Contribution

It introduces a new representation for compact operators between reflexive Banach spaces, broadening the scope of existing theories and including operators similar to those on Hilbert spaces.

Findings

Generalized representation for compact operators between reflexive Banach spaces.

Extension of Edmunds et al.'s results to broader classes of Banach spaces.

Illustrative example demonstrating the applicability of the new representation.

Abstract

In this article, we give a representation for compact operators acting between reflexive Banach spaces, which generalizes the representation given by Edmunds et al. for compact operators between reflexive Banach spaces with strictly convex duals. Further, we give a representation for operators on Banach spaces that are comparable to compact normal operators on Hilbert spaces and illustrate our result with an example.