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

Abstract

In this paper, we extend a spherical variant of the Kowalski-S\{l}odkowski 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.

References in corpus (2)

• 2-local isometries on function spaces
• On 2-local nonlinear surjective isometries on normed spaces and C${}^{\ast }$-algebras

Cited by in corpus (1)

• On 2-local nonlinear surjective isometries on normed spaces and C${}^{\ast }$-algebras