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Weak-2-local isometries on uniform algebras and Lipschitz algebras
Li, Lei (Nankai University (Xina). School of Mathematical Sciences)
Peralta Pereira, Antonio Miguel (Universidad de Granada. Departamento de Análisis Matemático)
Wang, Liguang (Qufu Normal University (Xina). School of Mathematical Sciences)
Wang, Ya-Shu (National Chung Hsing University (Taiwan). Department of Applied Mathematics)

Date: 2019
Abstract: We establish spherical variants of the Gleason–Kahane–Zelazko and Kowalski–S lodkowski theorems, and we apply them to prove that every weak-2-local isometry between two uniform algebras is a linear map. Among the consequences, we solve a couple of problems posed by O. Hatori, T. Miura, H. Oka, and H. Takagi in 2007. Another application is given in the setting of weak-2-local isometries between Lipschitz algebras by showing that given two metric spaces E and F such that the set Iso((Lip(E), k·k), (Lip(F), k·k)) is canonical, then every weak-2-local Iso((Lip(E), k · k), (Lip(F), k · k))-map ∆ from Lip(E) to Lip(F) is a linear map, where k · k can indistinctly stand for kfkL := max{L(f), kfk∞} or kfks := L(f) + kfk∞.
Rights: Tots els drets reservats
Language: Anglès.
Document: article ; recerca ; publishedVersion
Subject: 2-local isometries ; Uniform algebras ; Lipschitz functions ; Spherical Gleason–Kahane–Zelazko theorem ; Spherical Kowalski–Slodkowski theorem ; Weak-2-local isometries
Published in: Publicacions matemàtiques, Vol. 63 Núm. 1 (2019) , p. 241-264 (Articles) , ISSN 2014-4350

Adreça original: https://www.raco.cat/index.php/PublicacionsMatematiques/article/view/347137
DOI: 10.5565/PUBLMAT6311908

24 p, 410.2 KB

The record appears in these collections:
Articles > Published articles > Publicacions matemàtiques
Articles > Research articles

 Record created 2019-01-08, last modified 2019-02-02

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