2-local isometries on function spaces

2018/12/26 by Osamu Hatori, Hatori, Osamu, Shiho Oi +1 · 1 citation
Mathematics · #46B04 #46J10 #46J15 #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1812.10342

openalex publication_date 2018/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study 2-local reflexivity of the set of all surjective isometries between certain function spaces. We do not assume linearity for isometries. We prove that a 2-local isometry in the group of all surjective isometries on the algebra of all continuously differentiable functions on the closed unit interval with respect to several norms is a surjective isometry. We also prove that a 2-local isometry in the group of all surjective isometries on the Banach algebra of all Lipschitz functions on the closed unit interval with the sum-norm is a surjective isometry.

Cited by

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

Related

• 2-local standard isometries on vector-valued Lipschitz function spaces
• A generalization of the Kowalski -S\l odkowski theorem and its application to 2-local maps on function spaces
• On 2-local nonlinear surjective isometries on normed spaces and C^*-algebras
• A representation of isometries on function spaces
• Reflexivity of the isometry group of some classical spaces