Note on distortion and Bourgain ℓ₁-index
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 , α < ω₁, contains either an arbitrarily distortable subspace or an -asymptotic subspace.