Birkhoff-James extensions of continuous functions on metric spaces

Saptak Bhattacharya

Birkhoff-James extensions of continuous functions on metric spaces

Functional Analysis 2021-08-31 v1

Authors: Saptak Bhattacharya

Abstract

In this paper, we extend the investigations regarding Birkhoff-James orthogonality of linear operators to bounded continuous functions on metric spaces. We introduce Birkhoff-James extensions of continuous functions and study them in detail, in the separate contexts of compact and non-compact metric spaces. We conclude by discussing an application of our ideas to the study of Birkhoff-James orthogonality in $C(X)$ with the supremum norm, where $X$ is a compact metric space.

Keywords

extension theorems banach space function spaces and inequalities

Cite

@article{arxiv.2108.12576,
  title  = {Birkhoff-James extensions of continuous functions on metric spaces},
  author = {Saptak Bhattacharya},
  journal= {arXiv preprint arXiv:2108.12576},
  year   = {2021}
}

Comments

9 pages, 0 figures

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