Rigidity of commuting affine actions on reflexive Banach spaces

2012/07/16 by Rosendal, Christian
#FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1207.3731

Abstract

We give a simple argument to show that if α is an affine isometric action of a product G x H of topological groups on a reflexive Banach space X with linear part π, then either π(H) fixes a unit vector or α|G almost fixes a point on X. It follows that any affine isometric action of an abelian group on a reflexive Banach space X, whose linear part fixes no unit vectors, almost fixes points on X.

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