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

Volume 91 / 2010

Alistair Bird, Niels Jakob Laustsen Banach Center Publications 91 (2010), 45-76 MSC: Primary 46B45; Secondary 46B03, 47B37. DOI: 10.4064/bc91-0-3

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.

Authors

  • Alistair BirdDepartment of Mathematics and Statistics
    Lancaster University
    Lancaster LA1 4YF, England
    e-mail
  • Niels Jakob LaustsenDepartment of Mathematics and Statistics
    Lancaster University
    Lancaster LA1 4YF, England
    e-mail

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