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

Shiho Oi

Published 2019-03-27Version 1

In this paper, we extend a spherical variant of the Kowalski-S\{l}odkowski theorem due to Li, Peralta, Wang and Wang \cite{lpww}. 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.