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## Koliha–Drazin invertibles form a regularity

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:uir.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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