The Birkhoff-James orthogonality of operators on infinite dimensional Banach spaces

초록

We study the Birkhoff-James orthogonality on operator spaces in terms of the Bhatia-Semrl property. We first prove that every functional on a Banach space X has the Bhatia-Semrl property if and only if X is reflexive. We also find some geometric conditions of Banach space which ensure the denseness of operators with Bhatia-Semrl property. Finally, we investigate operators with the Bhatia-Semrl property when a domain space is L-1[0, 1] or C[0, 1]. (C) 2019 Elsevier Inc. All rights reserved.

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