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arXiv:2108.12576 [math.FA]AbstractReferencesReviewsResources

Birkhoff-James extensions of continuous functions on metric spaces

Saptak Bhattacharya

Published 2021-08-28Version 1

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.

Comments: 9 pages, 0 figures
Categories: math.FA
Subjects: 26A51, 54E45, 46B20
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