Web of Science: 4 cites, Scopus: 6 cites, Google Scholar: cites
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)

Data: 2019
Resum: 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∞.
Drets: Tots els drets reservats
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: 2-local isometries ; Uniform algebras ; Lipschitz functions ; Spherical Gleason-Kahane-Zelazko theorem ; Spherical Kowalski-Slodkowski theorem ; Weak-2-local isometries
Publicat a: 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
Adreça alternativa: https://www.raco.cat/index.php/PublicacionsMatematiques/article/view/347137/438201
DOI: 10.5565/PUBLMAT6311908


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