Operator norm localization property of relative hyperbolic group and graph of groups

In this article we study the spaces which have operator norm localization property. We prove that a finitely generated group Gamma which is strongly hyperbolic with respect to a collection of finitely generated subgroups (H-1,..., H-n) has operator norm localization property if and only if each H-i, i = 1, 2,..., n, has operator norm localization property. Furthermore we prove the following result. Let pi be the fundamental group of a connected finite graph of groups with finitely generated vertex groups G(P). If G(P) has operator norm localization property for all vertices P then pi has operator norm localization property. (C) 2008 Elsevier Inc. All rights reserved.