Rigidity of Commuting Affine Actions on Reflexive Banach Spaces
نویسنده
چکیده
We give a simple argument to show that if α is an affine isometric action of a product G ×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 if π is an isometric linear representation of a topological group G on a reflexive space X such that π(Z(G)) has no fixed unit vectors, then the reduced cohomology vanishes, i.e., H(G,π)= 0. 1. LINEAR REPRESENTATIONS AND COCYCLES When X is a vector space, the group of bijective affine transformations of X , Aff(X ), can be decomposed as a semidirect product
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