Benjamin, Ronalda and Laustsen, Niels Jakob and Mouton, Sonja
(2019)
*r-Fredholm theory in Banach algebras.*
Glasgow Mathematical Journal, 61 (3).
pp. 615-627.
ISSN 0017-0895

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## Abstract

Harte (Mathematische Zeitschrift, 1982) initiated the study of Fredholm theory relative to a unital homomorphism T: A→B between unital Banach algebras A and B based on the following notions: an element a∈A is called Fredholm if 0 is not in the spectrum of Ta, while a is Weyl (Browder) if there exist (commuting) elements b and c in A with a = b+c such that 0 is not in the spectrum of b and c is in the null space of T. We introduce and investigate the concepts of r-Fredholm, r-Weyl and r-Browder elements, where 0 in these definitions is replaced by the spectral radii of a and b, respectively.