paper

Birkhoff-James orthogonality in complex Banach spaces and Bhatia-Šemrl Theorem revisited

arXiv:2109.12775

Abstract

We explore Birkhoff-James orthogonality of two elements in a complex Banach space by using the directional approach. Our investigation illustrates the geometric distinctions between a smooth point and a non-smooth point in a complex Banach space. As a concrete outcome of our study, we obtain a new proof of the Bhatia-Šemrl Theorem on orthogonality of linear operators.

15 pages, 3 figures