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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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r-Fredholm theory in Banach algebras

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r-Fredholm theory in Banach algebras. / Benjamin, Ronalda; Laustsen, Niels Jakob; Mouton, Sonja.
In: Glasgow Mathematical Journal, Vol. 61, No. 3, 01.09.2019, p. 615-627.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Benjamin, R, Laustsen, NJ & Mouton, S 2019, 'r-Fredholm theory in Banach algebras', Glasgow Mathematical Journal, vol. 61, no. 3, pp. 615-627. https://doi.org/10.1017/S0017089518000393

APA

Benjamin, R., Laustsen, N. J., & Mouton, S. (2019). r-Fredholm theory in Banach algebras. Glasgow Mathematical Journal, 61(3), 615-627. https://doi.org/10.1017/S0017089518000393

Vancouver

Benjamin R, Laustsen NJ, Mouton S. r-Fredholm theory in Banach algebras. Glasgow Mathematical Journal. 2019 Sept 1;61(3):615-627. Epub 2018 Sept 25. doi: 10.1017/S0017089518000393

Author

Benjamin, Ronalda ; Laustsen, Niels Jakob ; Mouton, Sonja. / r-Fredholm theory in Banach algebras. In: Glasgow Mathematical Journal. 2019 ; Vol. 61, No. 3. pp. 615-627.

Bibtex

@article{69621ad485b74b22b6b9e8768dacafe1,
title = "r-Fredholm theory in Banach algebras",
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.",
keywords = "Fredholm, Weyl and Browder elements, Spectral theory, spectral radius, holomorphic function calculus",
author = "Ronalda Benjamin and Laustsen, {Niels Jakob} and Sonja Mouton",
note = "The final, definitive version of this article has been published in the Journal, Glasgow Mathematical Journal, 61 (3), pp 615-627 2004, {\textcopyright} 2018 Cambridge University Press.",
year = "2019",
month = sep,
day = "1",
doi = "10.1017/S0017089518000393",
language = "English",
volume = "61",
pages = "615--627",
journal = "Glasgow Mathematical Journal",
issn = "0017-0895",
publisher = "Cambridge University Press",
number = "3",

}

RIS

TY - JOUR

T1 - r-Fredholm theory in Banach algebras

AU - Benjamin, Ronalda

AU - Laustsen, Niels Jakob

AU - Mouton, Sonja

N1 - 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.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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.

AB - 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.

KW - Fredholm, Weyl and Browder elements

KW - Spectral theory

KW - spectral radius

KW - holomorphic function calculus

U2 - 10.1017/S0017089518000393

DO - 10.1017/S0017089518000393

M3 - Journal article

VL - 61

SP - 615

EP - 627

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

SN - 0017-0895

IS - 3

ER -