Property Fℓub>qub> implies property Fℓub>pub> for 1 < p < q < ∞

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• 作者：Alan Czuroń ^{alanczuron@gmail.com}
• 关键词：Fℓub>pFℓp property ; Kazhdan's property (T) ; Serre's fixed point property ; Affine isometric action ; 1-cohomology
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：307
• 期：Complete
• 页码：715-726
• 全文大小：304 K
• 卷排序：307

文摘

It is known that for σ-compact groups Kazhdan's Property (T) is equivalent to Serre's Property FH  . Generalized versions of those properties, called properties (TB)(TB) and FB, can be defined in terms of the isometric representations of a group on an arbitrary Banach space B. Property FB   implies (TB)(TB).It is known that a group with Property (Tℓub>p)(Tℓp) shares some properties with Kazhdan's groups, for example compact generation and compact abelianization. Moreover in the case of discrete groups, Property (Tℓub>p)(Tℓp) implies Lubotzky's Property (τ).In this paper we prove that in the case of discrete groups and ℓub>p(N)ℓp(N) spaces, for 1<p<q<∞,p≠21<p<q<∞,p≠2, Property Fℓub>qFℓq implies Property Fℓub>pFℓp.