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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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.
|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|
|Deposited By:||Dr Niels Jakob Laustsen|
|Deposited On:||08 Feb 2011 10:09|
|Last Modified:||19 Apr 2016 00:15|
Available Versions of this Item
- An amalgamation of the Banach spaces associated with James and Schreier, Part I : Banach-space structure. (deposited 13 Dec 2010 16:06)
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