Koliha–Drazin invertibles form a regularity

• Main Author: Smit, Joukje Anneke
• Other Authors: Lindeboom, L. (Dr.)
• Format: Others
• Language: en
• Published: 2011
• Subjects: Banach algebra; Radical; Spectrum; Resolvent; Quasinilpotent; Nilpotent; Spectral idempotent; Isolated spectral point; Accumulation point; Regularity; Koliha-Drazin invertible; Quasipolar; KD-spectrum; D-spectrum; Laurent expansion; Poles of the resolvent; 511.322; Axiomatic set theory; Banach algebras; Spectrum analysis; Spectral sequences (Mathematics)
• Online Access: http://hdl.handle.net/10500/4905

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)