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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## On the structure of Banach spaces with an unconditional basic sequence

### Tom 182 / 2007

Studia Mathematica 182 (2007), 67-85 MSC: Primary 46B20; Secondary 46B15. DOI: 10.4064/sm182-1-4

#### Streszczenie

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.

#### Autorzy

• Razvan AniscaDepartment of Mathematical Sciences