Property and Property restricted to a representation without non-zero invariant vectors

  • Mamoru Tanaka

    Tohoku University, Sendai, Japan

Abstract

In this paper, we give a necessary and sufficient condition for a finitely generated group to have a property like Kazhdan's Property restricted to one isometric representation on a strictly convex Banach space without non-zero invariant vectors. Similarly, we give a necessary and sufficient condition for a finitely generated group to have a property like Property restricted to the set of the affine isometric actions whose linear part is a given isometric representation on a strictly convex Banach space without non-zero invariant vectors. If the Banach space is the space on a finitely generated group, these conditions are regarded as an estimation of the spectrum of the -Laplace operator on the space and on the -Dirichlet finite space respectively.

Cite this article

Mamoru Tanaka, Property and Property restricted to a representation without non-zero invariant vectors. Groups Geom. Dyn. 8 (2014), no. 4, pp. 1141–1160

DOI 10.4171/GGD/258