Koliha–Drazin invertibles form a regularity

Smit, Joukje Anneke

dc.contributor.advisor	Lindeboom, Lucas
dc.contributor.author	Smit, Joukje Anneke
dc.date.accessioned	2011-10-06T07:46:30Z
dc.date.available	2011-10-06T07:46:30Z
dc.date.issued	2010-11
dc.date.submitted	2011-10-06
dc.identifier.citation	Smit, Joukje Anneke (2010) Koliha–Drazin invertibles form a regularity, University of South Africa, Pretoria, <http://hdl.handle.net/10500/4905>	en
dc.identifier.uri	http://hdl.handle.net/10500/4905
dc.description.abstract	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.	en
dc.format.extent	1 online resource (vi, 70 leaves)	en
dc.language.iso	en	en
dc.subject	Banach algebra	en
dc.subject	Radical	en
dc.subject	Spectrum	en
dc.subject	Resolvent	en
dc.subject	Quasinilpotent	en
dc.subject	Nilpotent	en
dc.subject	Spectral idempotent	en
dc.subject	Isolated spectral point	en
dc.subject	Accumulation point	en
dc.subject	Regularity	en
dc.subject	Koliha-Drazin invertible	en
dc.subject	Quasipolar	en
dc.subject	KD-spectrum	en
dc.subject	D-spectrum	en
dc.subject	Laurent expansion	en
dc.subject	Poles of the resolvent	en
dc.subject.ddc	511.322
dc.subject.lcsh	Axiomatic set theory	en
dc.subject.lcsh	Banach algebras	en
dc.subject.lcsh	Spectrum analysis	en
dc.subject.lcsh	Spectral sequences (Mathematics)	en
dc.title	Koliha–Drazin invertibles form a regularity	en
dc.type	Dissertation	en
dc.description.department	Mathematical Sciences	en
dc.description.degree	M. Sc. (Mathematics)