- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:00
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
8
2014
4
Property $(T_B)$ and Property $(F_B)$ restricted to a representation without non-zero invariant vectors
Mamoru
Tanaka
Tohoku University, SENDAI, JAPAN
Finitely generated groups, isometric action, strictly convex Banach spaces
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 $\ell \: ^p$ space (1
Group theory and generalizations
Functional analysis
Operator theory
1141
1160
10.4171/GGD/258
http://www.ems-ph.org/doi/10.4171/GGD/258