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

100%

Bird A.

Banach Center Publications

2010

tom 91

nr 1

35-43

The James-Schreier spaces, defined by amalgamating James' quasi-reflexive Banach spaces and Schreier space, can be equipped with a Banach-algebra structure. We answer some questions relating to their cohomology and ideal structure, and investigate the relations between them. In particular we show that the James-Schreier algebras are weakly amenable but not amenable, and relate these algebras to their multiplier algebras and biduals.

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

63%

Bird A., Laustsen N.

Banach Center Publications

2010

tom 91

nr 1

45-76

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 results include that each James-Schreier space is c₀-saturated and that no James-Schreier space embeds in a Banach space with an unconditional basis.

Ograniczanie wyników

2 Banach Center Publications

2 Bird A.

1 Laustsen N.

2 2010

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

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