A generalization of the Kowalski -S\l odkowski theorem and its application to 2-local maps on function spaces

2019/03/27 by Shiho Oi, Oi, Shiho
Mathematics · #30H05 #46B04 #46B20 #46J10 #46J15 #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1903.11424

openalex publication_date 2019/03/27 · openalex created_date 2019/04/01 · openalex updated_date 2026/07/28

Abstract

In this paper, we extend a spherical variant of the Kowalski-S\lodkowski theorem due to Li, Peralta, Wang and Wang. As a corollary, we prove that every 2-local map in the set of all surjective isometries (without assuming linearity) on a certain function space is in fact a surjective isometry. This gives an affirmative answer to the problem on 2-local isometries posed by Molnár.

Citations

• 2-local isometries on function spaces

Related

• 2-local isometries on function spaces
• Weak-2-local isometries on uniform algebras and Lipschitz algebras
• On 2-local nonlinear surjective isometries on normed spaces and C^*-algebras
• 2-local standard isometries on vector-valued Lipschitz function spaces
• On a problem of Mazur and Sternbach