Displaying similar documents to “Isomorphic Schauder decompositions in certain Banach spaces”

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.

Some problems on narrow operators on function spaces

Mikhail Popov, Evgenii Semenov, Diana Vatsek (2014)

Open Mathematics

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It is known that if a rearrangement invariant (r.i.) space E on [0, 1] has an unconditional basis then every linear bounded operator on E is a sum of two narrow operators. On the other hand, for the classical space E = L 1[0, 1] having no unconditional basis the sum of two narrow operators is a narrow operator. We show that a Köthe space on [0, 1] having “lots” of nonnarrow operators that are sum of two narrow operators need not have an unconditional basis. However, we do not know if...

RNP and KMP are equivalent for some Banach spaces with shrinking basis

Ginés López, Juan Mena (1996)

Studia Mathematica

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We get a characterization of PCP in Banach spaces with shrinking basis. Also, we prove that the Radon-Nikodym and Krein-Milman properties are equivalent for closed, convex and bounded subsets of some Banach spaces with shrinking basis.