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Multipliers and approximation properties of groups

Abstract : This thesis focusses on some approximation properties which generalise amenability for locally compact groups. These properties are defined by means of multipliers of certain algebras associated to the groups. The first part is devoted to the study of the p-AP, which is an extension of the AP of Haagerup and Kraus to the context of operators on Lp spaces. The main result asserts that simple Lie groups of higher rank and finite centre do not satisfy p-AP for any p between 1 and infinity. The second part concentrates on radial Schur multipliers on graphs. The study of these objects is motivated by some connections with actions of discrete groups and weak amenability. The three main results give necessary and sufficient conditions for a function of the natural numbers to define a radial multiplier on different classes of graphs generalising trees. More precisely, the classes of graphs considered here are products of trees, products hyperbolic graphs and finite dimensional CAT(0) cube complexes.
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Submitted on : Tuesday, November 27, 2018 - 12:53:06 PM
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  • HAL Id : tel-01936300, version 1



Ignacio Vergara Soto. Multipliers and approximation properties of groups. Operator Algebras [math.OA]. Université de Lyon, 2018. English. ⟨NNT : 2018LYSEN042⟩. ⟨tel-01936300⟩



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