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arXiv · 2108.12576

Birkhoff-James extensions of continuous functions on metric spaces

Saptak Bhattacharya
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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.

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Saptak Bhattacharya. 2021-08-28. Birkhoff-James extensions of continuous functions on metric spaces. https://arxiv.org/abs/2108.12576

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