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

Abstract

We prove that, if the closed unit ball of a normed space $X$ has sufficiently many extreme points, then every mapping $\Phi$ from $X$ into itself with the following property is affine: For any pair of points in $X$, there exists a (not necessarily linear) surjective isometry on $X$ that coincides with $\Phi$ at the two points. We also consider surjectivity of such a mapping in some special cases including C${}^{\ast }$-algebras.

8 pages

References in corpus (2)

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

Cited by in corpus (1)

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