Note on distortion and Bourgain ℓ₁ index

2007/09/14 by Anna Maria Pelczar, Pelczar, Anna Maria
Mathematics · #46B03 (Secondary) #46B20 (Primary) #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B03 #msc:46B20

paper · pdf · doi:10.48550/arxiv.0709.2272

14 pages, remarks and references added

openalex publication_date 2007/09/14 · arxiv created 2008/03/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The relation between different notions measuring proximity to ℓ₁ and distortability of a Banach space is studied. The main result states that a Banach space, whose all subspaces have Bourgain ℓ₁ index greater than ω^α, α<ω₁, contains either an arbitrary distortable subspace or an ℓ₁^α-asymptotic subspace.

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