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 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. © 2008 Elsevier Inc. All rights reserved.