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

Research output: Contribution to journalJournal article

Published

Journal publication date12/2010
JournalBanach Center Publications
Volume91
Number of pages32
Pages45-76
Original languageEnglish

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.

Bibliographic note

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