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  • r FredholmteorieFinalGMJaug2018

    Rights statement: 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.

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    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

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r-Fredholm theory in Banach algebras

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<mark>Journal publication date</mark>1/09/2019
<mark>Journal</mark>Glasgow Mathematical Journal
Issue number3
Volume61
Number of pages13
Pages (from-to)615-627
Publication StatusPublished
Early online date25/09/18
<mark>Original language</mark>English

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.

Bibliographic note

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.