On subspaces of invariant vectors

2015/09/17 by Tatiana Shulman, Shulman, Tatiana
Mathematics · #22A25 #22D25 #46B99 #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Representation Theory (math.RT) #math.FA #math.GR #math.RT #msc:22A25 #msc:22D25 #msc:46B99

paper · pdf · doi:10.48550/arxiv.1509.05263

arxiv created 2015/09/17 · arxiv updated 2015/09/18

Abstract

Let X_π be the subspace of fixed vectors for a uniformly bounded representation π of a group G on a Banach space X. We study the problem of the existence and uniqueness of a subspace Y that complements X_π in X. Similar questions for G-invariant complement to X_π are considered. We prove that every non-amenable discrete group G has a representation with non-complemented X_π and find some conditions that provide an G-invariant complement. A special attention is given to representations on C(K) that arise from an action of G on a metric compact K.

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