Property Fℓ_q implies property Fℓ_p for 1 < p < q < ∞

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• 作者：Alan Czuroń ^{alanczuron@gmail.com}
• 关键词：Fℓ_{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 (Tℓ_{p)(Tℓp) shares some properties with Kazhdan's groups, for example compact generation and compact abelianization. Moreover in the case of discrete groups, Property (Tℓp)(Tℓp) implies Lubotzky's Property (τ).In this paper we prove that in the case of discrete groups and ℓp(N)ℓp(N) spaces, for 1<p<q<∞,p≠21<p<q<∞,p≠2, Property FℓqFℓq implies Property FℓpFℓp.}