r-Fredholm theory in Banach algebras

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.

Item Type:
Journal Article
Journal or Publication Title:
Glasgow Mathematical Journal
Additional Information:
The final, definitive version of this article has been published in the Journal, Glasgow Mathematical Journal, 61 (3), pp 615-627 2004, © 2018 Cambridge University Press.
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/aacsb/disciplinebasedresearch
Subjects:
ID Code:
127119
Deposited By:
Deposited On:
29 Aug 2018 08:46
Refereed?:
Yes
Published?:
Published
Last Modified:
27 Sep 2020 04:44