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In this article poles, isolated spectral points, group, Drazin andKoliha-Drazin invertible elements in the context of quotient Banach algebras orin ranges of (not necessarily continuous) homomorphism between complex unitalBanach algebras will be characterized using Fredholm and Riesz Banach algebraelements. Calkin algebras on Banach and Hilbert spaces will be also considered.

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