Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.556186
Title: Factorial functionals and primal ideals of JB*-triples
Author: Hoskin, Factorial
Awarding Body: Oxford University
Current Institution: University of Oxford
Date of Award: 2004
Availability of Full Text:
Full text unavailable from EThOS.
Please contact the current institution’s library for further details.
Abstract:
The research presented in this thesis furthers the ongoing investigation into the structure of JB*-triples, an important class of Banach space with appli- cations to many areas of mathematics and mathematical physics. The thesis initiates the study of the connected theories of factorial functionals and primal ideals in the general JB*-triple situation and then gives applications of these theories, including: a non-abelian analogue of the Gelfand representation over a base space of minimal primal ideals; an investigation into the primitivity of minimal primal ideals; a characterisation of prime JB*-triples in terms of finite factorial function- als; a necessary condition on the factorial functionals for a JB*-triple to be antiliminal; a characterisation of elements in the pure functional space of a continuous JBW*-triple. Application (i) provides a tool for studying the structure of a class of JB*- triples. In particular it applies to JBW*-triples. Applications (i) and (ii) lead to a Gelfand representation of Type I JBW*-triples with primitive fibres. Ap- plications (iii) and (iv) are connected to Stone- Weierstrass theorems for JB*- triples. Application (v) is of interest because of the theoretical importance of pure functionals, and because pure functionals represent the pure states in quantum mechanical models.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.556186  DOI: Not available
Share: