The version for compact operators of Lindenstrauss properties A and B

TL;DR

This paper explores the properties of compact operators between Banach spaces, introducing analogues of Lindenstrauss properties A and B, and discusses conditions under which these operators can be approximated by norm attaining operators.

Contribution

It introduces the compact operator analogues of Lindenstrauss properties A and B and provides conditions for approximability by norm attaining operators.

Findings

Existence of compact operators not approximable by norm attaining operators

Conditions ensuring approximation of compact operators by norm attaining operators

Introduction of Lindenstrauss property analogues for compact operators

Abstract

It has been very recently discovered that there are compact linear operators between Banach spaces which cannot be approximated by norm attaining operators. The aim of this expository paper is to give an overview of those examples and also of sufficient conditions ensuring that compact linear operators can be approximated by norm attaining operators. To do so, we introduce the analogues for compact operators of Lindenstrauss properties A and B.