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

• Autorzy: Alistair Bird , Niels Jakob Laustsen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 46B45: Banach sequence spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 91
• Numer: 1
• Strony: 45-76

Daty

wydano

2010

Twórcy

autor

Alistair Bird

• Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England

autor

Niels Jakob Laustsen

• Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England

Identyfikatory

DOI

10.4064/bc91-0-3