On the cohomology of weakly almost periodic group representations

2013/02/06 by Uri Bader, Bader, Uri, Christian Rosendal +3
Mathematics · #22D12 #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #math.FA #math.GR #msc:22D12

paper · pdf · doi:10.48550/arxiv.1302.1392

added more references; 11 pages

arxiv created 2013/02/11 · arxiv updated 2013/02/12

Abstract

We initiate a study of cohomological aspects of weakly almost periodic group representations on Banach spaces, in particular, isometric representations on reflexive Banach spaces. Using the Ryll-Nardzewski fixed point Theorem, we prove a vanishing result for the restriction map (with respect to a subgroup) in the reduced cohomology of weakly periodic representations. Combined with the Alaoglu-Birkhoff decomposition theorem, this generalizes and complements theorems on continuous group cohomology by several authors.

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