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Note on distortion and Bourgain ℓ₁-index

Anna Maria Pelczar — 2009

Studia Mathematica

Relations between different notions measuring proximity to ℓ₁ and distortability of a Banach space are studied. The main result states that a Banach space all of whose subspaces have Bourgain ℓ₁-index greater than $ω^{α}$ , α < ω₁, contains either an arbitrarily distortable subspace or an $ℓ ₁^{α}$ -asymptotic subspace.

Some version of Gowers' dichotomy for Banach spaces.

Pelczar, Anna Maria — 2003

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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