Perturbation Ideals and Fredholm Theory in Banach Algebras
DOI:
https://doi.org/10.17398/2605-5686.37.1.91Palabras clave:
Fredholm elements, Index theory, Perturbation ideals, (semi)regularities, Riesz elementsResumen
In this paper we characterize perturbation ideals of sets that generate the familiar spectra in Fredholm theory.
Descargas
Referencias
P. Aiena, “Fredholm and Local Spectral Theory, with Applications to Multipliers”, Kluwer Academic Publishers, Dordrecht, 2004.
B. Aupetit, “A Primer on Spectral Theory”, Second edition, Springer-Verlag, New York, 1991.
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.
J.J. Grobler, H. Raubenheimer, The Index for Fredholm Elements in a Banach Algebra via Trace, Studia Mathematica 187 (3) (2008), 281 – 297.
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.
R. Harte, Fredholm Theory Relative to a Banach Algebra Homomorphism, Mathematische Zeitschrift 179 (1982), 431 – 436.
R. Harte, “Invertibility and Singularity for Bounded Linear Operators”, Marcel Dekker, New York-Basel, 1988.
J.J. Koliha, A Generalized Drazin Inverse, Glasgow Mathematical Journal 38 (3) (1996), 367 – 381.
V. Kordula, V. Müller, On the Axiomatic Theory of Spectrum, Studia Mathematica 119 (1996), 109 – 128.
A. Lebow, M. Schechter, Semigroups of Operators and Measures of Non-compactness, Journal of Functional Analysis 7 (1971), 1 – 26.
L. Lindeboom, H. Raubenheimer, On Regularities and Fredholm Theory, Czechoslovak Mathematical Journal 52 (2002), 565 – 574.
R.A. Lubansky, Koliha-Drazin Invertibles Form a Regularity, Proceedings of the Royal Irish Academy 107A (2) (2007), 137 – 141.
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.
H. du T. Mouton, S. Mouton, H. Raubenheimer, Ruston Elements and Fredholm Theory Relative to Arbitrary Homomorphisms, Quaestiones Mathematicae 34 (2011), 341 – 359.
V. Müller, Axiomatic Theory of Spectrum III - Semiregularities, Studia Mathematica 142(2) (2000), 159 – 169.
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.
M.R.F. Smyth, Riesz Theory in Banach Algebras, Mathematische Zeitschrift 145 (1975), 145 – 155.
W. Żelazko, Axiomatic approach to joint spectra I, Studia Mathematica 64 (1979), 249 – 261.
