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 add...
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| Format: | Others |
| Language: | en |
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2011
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| Online Access: | Smit, Joukje Anneke (2010) Koliha–Drazin invertibles form a regularity, University of South Africa, Pretoria, <http://hdl.handle.net/10500/4905> http://hdl.handle.net/10500/4905 |
| Summary: | 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) |
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