English

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

Functional Analysis 2019-07-17 v3

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 Moln\'ar.

Keywords

Cite

@article{arxiv.1903.11424,
  title  = {A generalization of the Kowalski -S\{l} odkowski theorem and its application to 2-local maps on function spaces},
  author = {Shiho Oi},
  journal= {arXiv preprint arXiv:1903.11424},
  year   = {2019}
}