Weak-2-local isometries on uniform algebras and Lipschitz algebras
- Li, Lei
- Peralta Pereira, Antonio Miguel
- Wang, Liguang
- Wang, Ya-Shu
ISSN: 0214-1493
Año de publicación: 2019
Volumen: 63
Número: 1
Páginas: 241-264
Tipo: Artículo
Otras publicaciones en: Publicacions matematiques
Resumen
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∞.
Información de financiación
L. Li was partly supported by NSF of China project no. 11301285. A. M. Peralta was partially supported by the Spanish Ministry of Economy and Competitiveness and European Regional Development Fund project no. MTM2014-58984-P and Junta de Andalucía grant FQM375. L. Wang was partly supported by NSF of China Grants No. 11371222, 11871303, and 11671133. Y.-S. Wang was partly supported by Taiwan MOST 104-2115-M-005-001-MY2.Financiadores
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National Natural Science Foundation of China
China
- 11871303
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Ministry of Science and Technology of the People's Republic of China
China
- 104-2115-M-005-001-MY2
- European Regional Development Fund European Union