Perturbation Ideals and Fredholm Theory in Banach Algebras
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Abstract
In this paper we characterize perturbation ideals of sets that generate the familiar spectra in Fredholm theory.
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How to Cite
Lukoto, T., & Raubenheimer, H. (2022). Perturbation Ideals and Fredholm Theory in Banach Algebras. Extracta Mathematicae, 37(1), 91-110. https://doi.org/10.17398/2605-5686.37.1.91
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Section
Operator Theory
References
[1] P. Aiena, “Fredholm and Local Spectral Theory, with Applications to Multipliers”, Kluwer Academic Publishers, Dordrecht, 2004.
[2] B. Aupetit, “A Primer on Spectral Theory”, Second edition, Springer-Verlag, New York, 1991.
[3] B.A. Barnes, G.J. Murphy, M.R.F. Smyth, T.T. West, “Riesz and Fredholm Theory in Banach Algebras”, Pitman, Boston-London-Melbourne, 1982.
[4] J.J. Grobler, H. Raubenheimer, The Index for Fredholm Elements in a Banach Algebra via Trace, Studia Mathematica 187 (3) (2008), 281 – 297.
[5] J.J. Grobler, H. Raubenheimer, A. Swartz, The Index for Fredholm Elements in a Banach Algebra via Trace II, Czechoslovac Mathematical Journal 66 (2016), 205 – 211.
[6] R. Harte, Fredholm Theory Relative to a Banach Algebra Homomorphism, Mathematische Zeitschrift 179 (1982), 431 – 436.
[7] R. Harte, “Invertibility and Singularity for Bounded Linear Operators”, Marcel Dekker, New York-Basel, 1988.
[8] J.J. Koliha, A Generalized Drazin Inverse, Glasgow Mathematical Journal 38 (3) (1996), 367 – 381.
[9] V. Kordula, V. Müller, On the Axiomatic Theory of Spectrum, Studia Mathematica 119 (1996), 109 – 128.
[10] A. Lebow, M. Schechter, Semigroups of Operators and Measures of Non-compactness, Journal of Functional Analysis 7 (1971), 1 – 26.
[11] L. Lindeboom, H. Raubenheimer, On Regularities and Fredholm Theory, Czechoslovak Mathematical Journal 52 (2002), 565 – 574.
[12] R.A. Lubansky, Koliha-Drazin Invertibles Form a Regularity, Proceedings of the Royal Irish Academy 107A (2) (2007), 137 – 141.
[13] H. du T. Mouton, H. Raubenheimer, More on Fredholm Theory Relative to a Banach Algebra Homomorphism, Proceedings of the Royal Irish Academy 93A (1) (1993), 17 – 25.
[14] H. du T. Mouton, S. Mouton, H. Raubenheimer, Ruston Elements and Fredholm Theory Relative to Arbitrary Homomorphisms, Quaestiones Mathematicae 34 (2011), 341 – 359.
[15] V. Müller, Axiomatic Theory of Spectrum III - Semiregularities, Studia Mathematica 142(2) (2000), 159 – 169.
[16] V. Müller, “Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras, Operator Theory Advances and Applications”, Vol. 139, Birkhäuser Verlag, Basel-Boston-Berlin, 2007.
[17] M.R.F. Smyth, Riesz Theory in Banach Algebras, Mathematische Zeitschrift 145 (1975), 145 – 155.
[18] W. Żelazko, Axiomatic approach to joint spectra I, Studia Mathematica 64 (1979), 249 – 261.
[2] B. Aupetit, “A Primer on Spectral Theory”, Second edition, Springer-Verlag, New York, 1991.
[3] B.A. Barnes, G.J. Murphy, M.R.F. Smyth, T.T. West, “Riesz and Fredholm Theory in Banach Algebras”, Pitman, Boston-London-Melbourne, 1982.
[4] J.J. Grobler, H. Raubenheimer, The Index for Fredholm Elements in a Banach Algebra via Trace, Studia Mathematica 187 (3) (2008), 281 – 297.
[5] J.J. Grobler, H. Raubenheimer, A. Swartz, The Index for Fredholm Elements in a Banach Algebra via Trace II, Czechoslovac Mathematical Journal 66 (2016), 205 – 211.
[6] R. Harte, Fredholm Theory Relative to a Banach Algebra Homomorphism, Mathematische Zeitschrift 179 (1982), 431 – 436.
[7] R. Harte, “Invertibility and Singularity for Bounded Linear Operators”, Marcel Dekker, New York-Basel, 1988.
[8] J.J. Koliha, A Generalized Drazin Inverse, Glasgow Mathematical Journal 38 (3) (1996), 367 – 381.
[9] V. Kordula, V. Müller, On the Axiomatic Theory of Spectrum, Studia Mathematica 119 (1996), 109 – 128.
[10] A. Lebow, M. Schechter, Semigroups of Operators and Measures of Non-compactness, Journal of Functional Analysis 7 (1971), 1 – 26.
[11] L. Lindeboom, H. Raubenheimer, On Regularities and Fredholm Theory, Czechoslovak Mathematical Journal 52 (2002), 565 – 574.
[12] R.A. Lubansky, Koliha-Drazin Invertibles Form a Regularity, Proceedings of the Royal Irish Academy 107A (2) (2007), 137 – 141.
[13] H. du T. Mouton, H. Raubenheimer, More on Fredholm Theory Relative to a Banach Algebra Homomorphism, Proceedings of the Royal Irish Academy 93A (1) (1993), 17 – 25.
[14] H. du T. Mouton, S. Mouton, H. Raubenheimer, Ruston Elements and Fredholm Theory Relative to Arbitrary Homomorphisms, Quaestiones Mathematicae 34 (2011), 341 – 359.
[15] V. Müller, Axiomatic Theory of Spectrum III - Semiregularities, Studia Mathematica 142(2) (2000), 159 – 169.
[16] V. Müller, “Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras, Operator Theory Advances and Applications”, Vol. 139, Birkhäuser Verlag, Basel-Boston-Berlin, 2007.
[17] M.R.F. Smyth, Riesz Theory in Banach Algebras, Mathematische Zeitschrift 145 (1975), 145 – 155.
[18] W. Żelazko, Axiomatic approach to joint spectra I, Studia Mathematica 64 (1979), 249 – 261.