Weak-2-local isometries on uniform algebras and Lipschitz algebras
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Universitat Autònoma de Barcelona
Li, L., Peralta, A. M., Wang, L., & Wang, Y. S. (2019). Weak-2-local isometries on uniform algebras and Lipschitz algebras. Publicacions Matemàtiques, 63(1), 241-264.
SponsorshipL. 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 Re- gional 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.
We establish spherical variants of the Gleason-Kahane-Zelazko and Kowalski-Slodkowski 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.