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 (Tℓp)(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.