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: | 26 Jul 2012 17:59 |
| Identification Number: | |
| URI: | http://eprints.lancs.ac.uk/id/eprint/39691 |
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