Property (TLΦ) and property (FLΦ) for Orlicz spaces LΦ

Mamoru Tanaka

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    An Orlicz space LΦ(Ω) is a Banach function space defined by using a Young function Φ, which generalizes the Lp spaces. We show, for an Orlicz space LΦ([0,1]) which is not isomorphic to L([0,1]), if a locally compact second countable group has property (TLΦ([0,1])), which is a generalization of Kazhdan's property (T) for linear isometric representations on LΦ([0,1]), then it has Kazhdan's property (T). We also show, for a separable complex Orlicz space LΦ(Ω) with gauge norm, Ω=R,[0,1],N, if a locally compact second countable group has Kazhdan's property (T), then it has property (TLΦ(Ω)). We prove, for a finitely generated group Γ and a Banach space B whose modulus of convexity is sufficiently large, if Γ has Kazhdan's property (T), then it has property (FB), which is a fixed point property for affine isometric actions on B. Moreover, we see that, for a hyperbolic group Γ (which may have Kazhdan's property (T)) and an Orlicz sequence space ℓΦΨ with gauge norm such that the Young function Ψ sufficiently rapidly increases near 0, Γ doesn't have property (FΦΨ). These results are generalizations of the results for Lp-spaces.

    Original languageEnglish
    Pages (from-to)1406-1434
    Number of pages29
    JournalJournal of Functional Analysis
    Volume272
    Issue number4
    DOIs
    Publication statusPublished - 2017 Feb 15

    Keywords

    • Kazhdan's property (T)
    • Locally compact second countable groups
    • Orlicz spaces

    ASJC Scopus subject areas

    • Analysis

    Fingerprint Dive into the research topics of 'Property (T<sub>L<sup>Φ</sup></sub>) and property (F<sub>L<sup>Φ</sup></sub>) for Orlicz spaces L<sup>Φ</sup>'. Together they form a unique fingerprint.

    Cite this