English

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