Isolated spectral points and Koliha-Drazin invertible elements in quotient Banach algebras and homomorphism ranges

Abstract

In this article, poles, isolated spectral points, group, Drazin and Koliha-Drazin invertible elements in the context of quotient Banach algebras or in ranges of (not necessarily continuous) homomorphisms between complex unital Banach algebras will be characterized using Fredholm and Riesz Banach algebra elements. The special cases of C*-algebras and Calkin algebras on Banach and Hilbert spaces will be also considered. In particular, a characterization of the isolated spectral points of the Fredholm spectrum of Banach and Hilbert space operators will be presented. Finally, the sets of Drazin and Koliha-Drazin invertible Calkin algebra elements will be described by means of classes of operators.