Some remarks on spreading models and mixed Tsirelson spaces

Abstract

Abstract. We prove that if a Banach space with a bimonotone shrinking basis does not contain ω 1 spreading models but every block sequence of the basis contains a further block sequence which is a c − n 1 spreading model for every n ∈ N, then every subspace has a further subspace which is arbitrarily distortable. We also prove that a mixed Tsirelson space T [(Sn, θn)n], such that θn 0, does not contain ω2 1 spreading models.