Uniqueness of some unconditional bases II

J. Lindenstrauss

Displaying similar documents to “Uniqueness of some unconditional bases II”

Aspects of unconditionality of bases in spaces of compact operators

James R. Holub (1998)

Annales Polonici Mathematici

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E. Tutaj has introduced classes of Schauder bases termed "unconditional-like" (UL) and "unconditional-like*" (UL*) whose intersection is the class of unconditional bases. In view of this association with unconditional bases, it is interesting to note that there exist Banach spaces which have no unconditional basis and yet have a basis of one of these two types (e.g., the space 𝓞[0,1]). In the same spirit, we show in this paper that the space of all compact operators on a reflexive Banach...

The Tsirelson space $𝒯 (p)$ has a unique unconditional basis up to permutation for $0 < p < 1$ .

Albiac, F., Leránoz, C. (2009)

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A simple proof of two theorems concerning bases of $C (0, 1)$

G. Schechtman (1978-1979)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

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On subspaces of locally convex spaces with unconditional Schauder bases

L. Drewnowski (1987)

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On projections and unconditional bases in direct sums of Banach spaces

I. Edelstein, P. Wojtaszczyk (1976)

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On the relation between several notions of unconditional structure - A counterexample

G. Schechtman (1978-1979)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

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Symmetric bases in Minkowski spaces

D. R. Lewis, P. Wojtaszczyk (1976)

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On the structure of separable $L_{p}$ spaces (1 < p < ∞)

D. Alspach, P. Enflo, E. Odell (1977)

Studia Mathematica

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Bases in the spaces $C$ and $L^{1}$

S. J. Szarek (1979-1980)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

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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.

On shrinking basic sequences in Banach spaces

David Dean, Ivan Singer, Leonard Stembach (1971)

Studia Mathematica

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Characterising subspaces of Banach spaces with a Schauder basis having the shift property

Christian Rosendal (2011)

Studia Mathematica

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We give an intrinsic characterisation of the separable reflexive Banach spaces that embed into separable reflexive spaces with an unconditional basis all of whose normalised block sequences with the same growth rate are equivalent. This uses methods of E. Odell and T. Schlumprecht.