Birkhoff-James orthogonality in complex Banach spaces and Bhatia-\v{S}emrl Theorem revisited
Functional Analysis
2021-09-28 v1
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-\v{S}emrl Theorem on orthogonality of linear operators.
Keywords
Cite
@article{arxiv.2109.12775,
title = {Birkhoff-James orthogonality in complex Banach spaces and Bhatia-\v{S}emrl Theorem revisited},
author = {Saikat Roy and Satya Bagchi and Debmalya Sain},
journal= {arXiv preprint arXiv:2109.12775},
year = {2021}
}
Comments
15 pages, 3 figures