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On the structure of Banach spaces with an unconditional basic sequence

Tom 182 / 2007

Razvan Anisca 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
    Lakehead University
    Thunder Bay, ON, Canada P7B 5E1
    e-mail

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