Orthogonality for Biadjoints of Operators

Document Type

Article

Publication Title

Indian Statistical Institute Series

Abstract

Let X, Y be non-reflexive Banach spaces. Let L(X, Y) be the space of bounded operators from X to Y. For T∈ L(X, Y), and a closed subspace Z⊂ Y, this paper deals with the question, if T⊥ L(X, Z) in the sense of Birkhoff-James, when is T∗ ∗⊥ L(X∗ ∗, Z⊥⊥) ? If Z⊂ Y is a subspace of finite codimension which is the kernel of projection of norm one, we show that this is always the case. Moreover in this case, there is an extreme point Λ of the unit ball of the bidual X∗ ∗ such that ‖ T∗ ∗‖ = ‖ T∗ ∗(Λ ) ‖ and T∗ ∗(Λ ) ⊥ Z⊥⊥.

First Page

191

Last Page

196

DOI

10.1007/978-981-99-2310-6_10

Publication Date

1-1-2023

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