Operator norm localization property of relative hyperbolic group and graph of groups |
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Authors: | Xiaoman Chen |
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Affiliation: | Department of Mathematics, Fudan University, Shanghai 200433, China |
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Abstract: | In this article we study the spaces which have operator norm localization property. We prove that a finitely generated group Γ which is strongly hyperbolic with respect to a collection of finitely generated subgroups {H1,…,Hn} has operator norm localization property if and only if each Hi, i=1,2,…,n, has operator norm localization property. Furthermore we prove the following result. Let π be the fundamental group of a connected finite graph of groups with finitely generated vertex groups GP. If GP has operator norm localization property for all vertices P then π has operator norm localization property. |
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Keywords: | Operator norm localization property Coarse invariant Roe algebras Finite propagation Strongly relative hyperbolic group Graph of groups |
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