Property (FL_p) implies property (FL_q) for 1

2014/09/16 by Czuron, Alan
#FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1409.4609

Abstract

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 (T_B) and (F_B), can be defined in terms of the isometric representations of a group on an arbitrary Banach space B. Property (F_B) implies (T_B). It is known that a group with Property (T_lp) shares some properties with Kazhdan's groups, for example compact generation and compact abelianization. Moreover in the case of discrete groups, Property (T_lp) implies Lubotzky's Property (τ). In this paper we prove that in the case of discrete groups and 1

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