Title page for ETD etd-12042006-123908


Document Type Doctoral Thesis
Author Bapela, Manas Majakwane
URN etd-12042006-123908
Document Title Riesz theory and Fredholm determinants in Banach algebras
Degree PhD (Mathematics)
Department Mathematics and Applied Mathematics
Supervisor
Advisor Name Title
Prof A Stroh Committee Chair
Prof J Swart Committee Co-Chair
Keywords
  • operator algebras
  • linear algebraic groups
Date 1999-10-01
Availability unrestricted
Abstract
In the classical theory of operators on a Banach space a beautiful interplay exists between Riesz and Fredholm theory, and the theory of traces and de¬terminants for operator ideals. In this thesis we obtain a complete Riesz de¬composition theorem for Riesz elements in a semi prime Banach algebra and on the other hand extend the existing theory of traces and determinants to a more general setting of Banach algebras.

In order to obtain some of these results we use the notion of finite multiplicity of spectral points to give a characterization of the essential spec¬trum for elements in a Banach algebra. As an immediate corollary we obtain the well-known characterization of Riesz elements namely that their non-zero spectral points are isolated and of finite multiplicities. In the final chapter of the thesis we use Plemelj's type formulas to define a determinant on the ideal of finite rank elements and show that it extends continuously to the ideal of nuclear elements.

© 1999, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.

Please cite as follows:

Bapela, MM 1999, Riesz theory and Fredholm determinants in Banach algebras, PhD thesis, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-12042006-123908/ >

H751/ag

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