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arXiv · 1207.3731

Rigidity of commuting affine actions on reflexive Banach spaces

Christian Rosendal
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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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Christian Rosendal. 2012-07-16. Rigidity of commuting affine actions on reflexive Banach spaces. https://arxiv.org/abs/1207.3731

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