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 AbstractIn 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.
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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/ >
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