Variants of a-T-menability for actions on non-commutative Lp spacesReport as inadecuate




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1 IRMAR - Institut de Recherche Mathématique de Rennes

Abstract : We investigate various characterizations of the Haagerup property H for a second countable locally compact group G, in terms of orthogonal representations of G on non-commutative Lp spaces. We introduce a variant H Lp for orthogonal representations with vanishing coefficients on Lp, and study its relationships with property H. We also give a characterization of H by the means of strongly mixing actions on a non-commutative Lp space. We construct proper actions of groups with H by affine isometries on some non-commutative Lp space, such as the Lp space associated to the hyperfinite II infinite factor.

Keywords : a-T-menabilty non-commutative Lp spaces orthogonal group representations property H proper actions by affine isometries





Author: Baptiste Olivier -

Source: https://hal.archives-ouvertes.fr/



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