Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.551626
Title: A study of James-Schreier spaces as Banach spaces and Banach algebras
Author: Bird, Alistair
Awarding Body: Lancaster University
Current Institution: Lancaster University
Date of Award: 2010
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Abstract:
We define and study a new family of Banach spaces, the J ames-Schreier spaces, cre- ated by combining key properties in the definitions of two important classical Banach spaces, namely James' quasi-reflexive space and Schreier's space. We explore both the Banach space and Banach algebra theory of these spaces. The new spaces inherit aspects of both parent spaces: our main results are that the J ames-Schreier spaces each have a shrinking basis, do not embed in a Banach space with an unconditional basis, and each of their closed, infinite-dimensional subspaces contains a copy of Co. As Banach sequence algebras each James-Schreier space has a bounded approx- imate identity and is weakly amenable but not amenable, and the bidual and multiplier - algebra are isometrically isomorphic. We approach our study of Banach sequence algebras from the point of view of Schauder basis theory, in particular looking at those Banach sequence algebras for which the unit vectors form an unconditional or shrinking basis. We finally show that for each Banach space X with an unconditional basis we may construct a James-like Banach sequence algebra j(X) with a bounded approximate identity, and give a condition on the shift operators acting on X which implies that j(X) will contain a copy of X as a complemented ideal and hence not be amenable.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.551626  DOI: Not available
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