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r-FREDHOLM THEORY IN BANACH ALGEBRAS

Published online by Cambridge University Press:  25 September 2018

RONALDA BENJAMIN*
Affiliation:
Department of Mathematical Sciences, Private Bag X1, Stellenbosch University, Matieland 7602, South Africa e-mail: [email protected]
NIELS JAKOB LAUSTSEN*
Affiliation:
Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster LA1 4YF, United Kingdom e-mail: [email protected]
SONJA MOUTON*
Affiliation:
Department of Mathematical Sciences, Private Bag X1, Stellenbosch University, Matieland 7602, South Africa e-mail: [email protected]
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Abstract

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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 aA 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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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