Geodesic
On the structure of Banach spaces with an unconditional basic sequence
Razvan Anisca1
1 Department of Mathematical Sciences Lakehead University Thunder Bay, ON, Canada P7B 5E1
Studia Mathematica, Tome 182 (2007) no. 1, pp. 67-85

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm182-1-4
Keywords: banach space unconditional basic sequence following regular irregular alternatives holds either contains subspace isomorphic ell contains subspace which has unconditional finite dimensional decomposition does admit decomposition uniform bound dimensions decomposition result viewed context gowers dichotomy theorem

Razvan Anisca 1

1 Department of Mathematical Sciences Lakehead University Thunder Bay, ON, Canada P7B 5E1 
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Razvan Anisca. On the structure of Banach spaces with an
 unconditional basic sequence. Studia Mathematica, Tome 182 (2007) no. 1, pp. 67-85. doi: 10.4064/sm182-1-4

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