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Displaying similar documents to “On the relation between several notions of unconditional structure - A counterexample”

On the structure of Banach spaces with an unconditional basic sequence

Razvan Anisca (2007)

Studia Mathematica

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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 ℓ₂, 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.

Subspaces of ℓ₂(X) and Rad(X) without local unconditional structure

Ryszard A. Komorowski, Nicole Tomczak-Jaegermann (2002)

Studia Mathematica

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It is shown that if a Banach space X is not isomorphic to a Hilbert space then the spaces ℓ₂(X) and Rad(X) contain a subspace Z without local unconditional structure, and therefore without an unconditional basis. Moreover, if X is of cotype r < ∞, then a subspace Z of ℓ₂(X) can be constructed without local unconditional structure but with 2-dimensional unconditional decomposition, hence also with basis.