On 2-local nonlinear surjective isometries on normed spaces and C*-algebras

Mori, Michiya

doi:10.1090/proc/14949

On 2-local nonlinear surjective isometries on normed spaces and C$^*$-algebras
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Proc. Amer. Math. Soc. 148 (2020), 2477-2485 Request permission

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$^*$-algebras.

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