The axiomatic theory of ` Zelazko defines a variety of general spectra where specified axioms
are satisfied. However, there arise a number of spectra, usually defined for a single element
of a Banach algebra, that are not covered by the axiomatic theory of ` Zelazko. V. Kordula and
V. M¨uller addressed this issue and created the theory of regularities. Their unique idea was
to describe the underlying set of elements on which the spectrum is defined. The axioms of a
regularity provide important consequences. We prove that the set of Koliha-Drazin invertible
elements, which includes the Drazin invertible elements, forms a regularity. The properties of
the spectrum corresponding to a regularity are also investigated. / Mathematical Sciences / M. Sc. (Mathematics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:umkn-dsp01.int.unisa.ac.za:10500/4905 |
| Date | 10 1900 |
| Creators | Smit, Joukje Anneke |
| Contributors | Lindeboom, L. (Dr.) |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | 1 online resource (vi, 70 leaves) |
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