Basic properties of pure functionals of a <I>C</I><sup>*</sup>-algebra are reviewed, and this is followed by an investigation of equivalent representations of a pure functional, restriction to ideals, and extension to bigger <I>C</I><sup>*</sup>-algebras. The relationship between notions of regularity for points in the spectrum of a <I>C</I><sup>*</sup>-algebra is studied. A localised version of Fell-Dixmier conditions for continuous trace of a <I>C</I><sup>*</sup>-algebra is obtained. The weak<sup>*</sup>-closure of the space of pure functionals of arbitrary and homogeneous <I>C</I><sup>*</sup>-algebras is investigated. An analogue of Glimm's Vector State Space Theorem is proved. It is shown that G(A) = A<sup>*</sup><sub>1</sub> if and only if <I>A</I> is prime and antiliminal. Some results about the limits of pure functionals of an arbitrary <I>C<sup>*</sup>-</I>algebra are obtained.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:302663 |
| Date | January 1998 |
| Creators | Shah, Masood Hussain |
| Publisher | University of Aberdeen |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=191155 |
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