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r-FREDHOLM THEORY IN BANACH ALGEBRAS

Part of: Topological algebras, normed rings and algebras, Banach algebras General theory of linear operators

Published online by Cambridge University Press:  25 September 2018

RONALDA BENJAMIN ,
NIELS JAKOB LAUSTSEN  and
SONJA MOUTON
RONALDA BENJAMIN*
Affiliation:
Department of Mathematical Sciences, Private Bag X1, Stellenbosch University, Matieland 7602, South Africa e-mail: ronalda@sun.ac.za
NIELS JAKOB LAUSTSEN*
Affiliation:
Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster LA1 4YF, United Kingdom e-mail: n.laustsen@lancaster.ac.uk
SONJA MOUTON*
Affiliation:
Department of Mathematical Sciences, Private Bag X1, Stellenbosch University, Matieland 7602, South Africa e-mail: smo@sun.ac.za
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Abstract

Harte (1982, Math. Z.179, 431–436) 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.

MSC classification

Primary: 46H30: Functional calculus in topological algebras
Secondary: 47A10: Spectrum, resolvent 47A53: (Semi-) Fredholm operators; index theories
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 3 , September 2019 , pp. 615 - 627
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

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