Ideal operators and relative Godun sets

Abstract

In this paper we study ideals in Banach spaces through ideal operators. We provide characterisation of recently introduced notion of almost isometric ideal which is a version of Principle of Local Reflexivity for a subspace of a Banach space. Studying ideals through ideal operators give us better insight in to the properties of these subspaces vis-a-vis properties of the space itself. We provide a few applications of our characterisation theorem.

Keywords

• Ideals
• almost isometric ideals
• strict ideals
• maximal ideal operator
• Godun sets
• VN-subspaces