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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: Article
    Journal or Publication Title: Banach Center Publications
    Additional Information: 2010 Mathematics Subject Classification: Primary 46B45; Secondary 46B03, 47B37.
    Uncontrolled Keywords: Banach space ; James space ; Schreier space ; shrinking basis ; shift operator ; c_0-saturation ; Pelczynski's property (u).
    Subjects: Q Science > 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: 09 Oct 2013 13:14
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/39691

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