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

Bird, Alistair and Laustsen, Niels Jakob (2010) An amalgamation of the Banach spaces associated with James and Schreier, Part I : Banach-space structure. Banach Center Publications, 91. pp. 45-76. ISSN 0137-6934

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Abstract

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 c_0-saturated and that no James-Schreier space embeds in a Banach space with an unconditional basis.

Item Type:

Journal Article

Journal or Publication Title:

Banach Center Publications

Additional Information:

2010 Mathematics Subject Classification: Primary 46B45; Secondary 46B03, 47B37.

Uncontrolled Keywords:

/dk/atira/pure/researchoutput/libraryofcongress/qa

Subjects:

?? banach spacejames spaceschreier spaceshrinking basisshift operatorc_0-saturationpelczynski's property (u).qa mathematics ??

Departments:

Faculty of Science and Technology > Mathematics and Statistics

ID Code:

39691

Deposited By:

Dr Niels Jakob Laustsen

Deposited On:

08 Feb 2011 10:09

Refereed?:

Yes

Published?:

Published

Last Modified:

29 Feb 2024 00:39

URI:

https://eprints.lancs.ac.uk/id/eprint/39691