Geodesic
Property $(T_B)$ and Property $(F_B)$ restricted to a representation without non-zero invariant vectors
Mamoru Tanaka1
1Tohoku University, Sendai, Japan
Groups, geometry, and dynamics, Tome 8 (2014) no. 4, pp. 1141-1160

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DOI

In this paper, we give a necessary and sufficient condition for a finitely generated group to have a property like Kazhdan's Property (T) 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 (FH) 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 lp space (1<p<∞) on a finitely generated group, these conditions are regarded as an estimation of the spectrum of the p-Laplace operator on the lp space and on the p-Dirichlet finite space respectively.
DOI : 10.4171/ggd/258
Classification : 20-XX, 46-XX, 47-XX
Mots-clés : Finitely generated groups, isometric action, strictly convex Banach spaces

Mamoru Tanaka  1

1 Tohoku University, Sendai, Japan 
Mamoru Tanaka. Property $(T_B)$ and Property $(F_B)$ restricted to a representation without non-zero invariant vectors. Groups, geometry, and dynamics, Tome 8 (2014) no. 4, pp. 1141-1160. doi: 10.4171/ggd/258
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     pages = {1141--1160},
     year = {2014},
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     number = {4},
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