Theti Property (TB) and Property (FB) restricted to a representation without non-zero invariant vectors

Mamoru Tanaka

    Research output: Contribution to journalArticlepeer-review

    Abstract

    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 ≤p space (1 < p < ∞) on a ffinitely generated group, these conditions are regarded as an estimation of the spectrum of the p-Laplace operator on the ≤p space and on the p-Dirichlet finite space respectively.

    Original languageEnglish
    Pages (from-to)1141-1160
    Number of pages20
    JournalGroups, Geometry, and Dynamics
    Volume8
    Issue number4
    DOIs
    Publication statusPublished - 2014

    Keywords

    • Finitely generated groups
    • Isometric action
    • Strictly convex Banach spaces

    ASJC Scopus subject areas

    • Geometry and Topology
    • Discrete Mathematics and Combinatorics

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