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

Mamoru Tanaka

    研究成果: Article査読

    4 被引用数 (Scopus)

    抄録

    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.

    本文言語English
    ページ(範囲)1406-1434
    ページ数29
    ジャーナルJournal of Functional Analysis
    272
    4
    DOI
    出版ステータスPublished - 2017 2月 15

    ASJC Scopus subject areas

    • 分析

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