Riesz theory and Fredholm determinants in Banach algebras

Loading...
Thumbnail Image

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

University of Pretoria

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.

Description

Thesis (PhD (Mathematics))--University of Pretoria, 2006.

Keywords

Operator algebras, Linear algebraic groups, UCTD

Sustainable Development Goals

Citation

Bapela, MM 1999, Riesz theory and Fredholm determinants in Banach algebras, PhD thesis, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/30088 >