2012/12/19 by Benben Liao, Liao, Benben
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Group Theory (math.GR) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.GR #math.OA
paper · pdf · doi:10.48550/arxiv.1212.4646
This text is an improved version of the author's master thesis
arxiv created 2012/12/19 · openalex publication_date 2012/12/19 · arxiv updated 2012/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This text takes, with more details and simplifying a proof in section 3, the parts of [Laf08] and [Laf09] treating p-adic groups. We prove that SL3 over a non archimedian local field F has strong Banach property (T). The applications are as follows: any connected almost F-simple algebraic group G over F whose Lie algebra contains sl3(F) has strong Banach property (T), the family of expanders constructed from a lattice of G(F) do not embed uniformly in any Banach space of type >1, and any isometric affine action of G(F) on a Banach space of type >1 admits a fix point.