On the structure of Banach spaces with an unconditional basic sequence
Volume 182 / 2007
Studia Mathematica 182 (2007), 67-85
MSC: Primary 46B20; Secondary 46B15.
DOI: 10.4064/sm182-1-4
Abstract
For a Banach space $X$ with an unconditional basic sequence, one of the following regular-irregular alternatives holds: either $X$ contains a subspace isomorphic to $\ell _2$, or $X$ contains a subspace which has an unconditional finite-dimensional decomposition, but does not admit such a decomposition with a uniform bound for the dimensions of the decomposition. This result can be viewed in the context of Gowers' dichotomy theorem.
