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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:556186 |
| Date | January 2004 |
| Creators | Hoskin, Factorial |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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