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

2019/07/04 by Mori, Michiya
#FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1907.02172

Abstract

We prove that, if the closed unit ball of a normed space X has sufficiently many extreme points, then every mapping Φ 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 Φ at the two points. We also consider surjectivity of such a mapping in some special cases including C^*-algebras.

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