Displaying similar documents to “Types of tightness in spaces with unconditional basis”

An amalgamation of the Banach spaces associated with James and Schreier, Part I: Banach-space structure

Alistair Bird, Niels Jakob Laustsen (2010)

Banach Center Publications

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We create a new family of Banach spaces, the James-Schreier spaces, by amalgamating two important classical Banach spaces: James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. We then investigate the properties of these James-Schreier spaces, paying particular attention to how key properties of their 'ancestors' (that is, the James space and the Schreier space) are expressed in them. Our main...

The basic sequence problem

N. Kalton (1995)

Studia Mathematica

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We construct a quasi-Banach space X which contains no basic sequence.

Incomparable, non-isomorphic and minimal Banach spaces

Christian Rosendal (2004)

Fundamenta Mathematicae

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A Banach space contains either a minimal subspace or a continuum of incomparable subspaces. General structure results for analytic equivalence relations are applied in the context of Banach spaces to show that if E₀ does not reduce to isomorphism of the subspaces of a space, in particular, if the subspaces of the space admit a classification up to isomorphism by real numbers, then any subspace with an unconditional basis is isomorphic to its square and hyperplanes, and the unconditional...

On strong M-bases in Banach spaces with PRI.

Deba P. Sinha (2000)

Collectanea Mathematica

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If every member of a class P of Banach spaces has a projectional resolution of the identity such that certain subspaces arising out of this resolution are also in the class P, then it is proved that every Banach space in P has a strong M-basis. Consequently, every weakly countably determined space, the dual of every Asplund space, every Banach space with an M-basis such that the dual unit ball is weak* angelic and every C(K) space for a Valdivia compact set K , has a strong M-basis. ...

1-amenability of 𝒜(X) for Banach spaces with 1-unconditional bases

A. Blanco (2012)

Studia Mathematica

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The main result of the note is a characterization of 1-amenability of Banach algebras of approximable operators for a class of Banach spaces with 1-unconditional bases in terms of a new basis property. It is also shown that amenability and symmetric amenability are equivalent concepts for Banach algebras of approximable operators, and that a type of Banach space that was long suspected to lack property 𝔸 has in fact the property. Some further ideas on the problem of whether or not amenability...