Tingley's problems on uniform algebras

Tingley's problems on uniform algebras

We prove that a surjective isometry between the unit spheres of two uniform algebras is extended to a surjective real-linear isometry between the uniform algebras. It provides the first positive solution to Tingley's problem on a Banach space, without being a Hilbert space, consisting of analyt...

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Veröffentlicht in:Journal of mathematical analysis and applications 2021-11, Vol.503 (2), p.125346, Article 125346
Hauptverfasser: Hatori, Osamu, Oi, Shiho, Shindo Togashi, Rumi
Format: Artikel
Sprache:eng
Schlagworte:
Analytic functions
Maximal convex sets
Surjective isometries
Tingley's problem
Uniform algebras
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Zusammenfassung:We prove that a surjective isometry between the unit spheres of two uniform algebras is extended to a surjective real-linear isometry between the uniform algebras. It provides the first positive solution to Tingley's problem on a Banach space, without being a Hilbert space, consisting of analytic functions.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.125346