Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T18:30:55.005Z Has data issue: false hasContentIssue false
  • English
  • Français

A generalized Drazin inverse

Published online by Cambridge University Press:  18 May 2009

J. J. Koliha
J. J. Koliha
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The main theme of this paper can be described as a study of the Drazin inverse for bounded linear operators in a Banach space X when 0 is an isolated spectral point ofthe operator. This inverse is useful for instance in the solution of differential equations formulated in a Banach space X. Since the elements of X rarely enter into our considerations, the exposition seems to gain in clarity when the operators are regarded as elements of the Banach algebra L(X).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 3 , September 1996 , pp. 367 - 381
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

REFERENCES

1.Ben-Israel, A. and Greville, T. N. E., Generalized Inverses: Theory and Applications (Wiley-Interscience, New York, 1974).Google Scholar
2.Bouldin, R. H., Generalized inverses and factorizations, in Recent Applications of Generalized Inverses, Campbell, S. L., ed., Research Notes in Mathematics 66 (Pitman, London, 1982), 233–249.Google Scholar
3.Campbell, S. L., The Drazin inverse of an operator, in Recent Applications of Generalized Inverses. Campbell, S. L., ed., Research Notes in Mathematics 66 (Pitman, London, 1982) 250–259.Google Scholar
4.Campbell, S. L. and Meyer, C. D., Generalized Inverses of Linear Transformations (Pitman, London, 1979).Google Scholar
5.Campbell, S. L., Meyer, C. D. and Rose, N. J., Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients, SIAM J. Appl. Math. 31 (1976), 411–425.CrossRefGoogle Scholar
6.Caradus, S. R., Generalized inverses and operator theory, Queen's Papers in Pure and Appl. Math. 50 (Queen's University, Kingston, Ontario, 1978).Google Scholar
7.Drazin, M. P., Pseudo-inverse in associative rings and semigroups, Amer. Math. Monthly 65 (1958), 506–514.CrossRefGoogle Scholar
8.Drazin, M. P., Extremal definitions of generalized inverses, Lin. Alg. Appl. 165 (1992), 185–196.CrossRefGoogle Scholar
9.Harte, R. E., Spectral projections, Irish Math. Soc. Newsletter 11 (1984), 10–15.CrossRefGoogle Scholar
10.Harte, R. E., Invertibility and Singularity for Bounded Linear Operators (Marcel Dekker, New York, 1988).Google Scholar
11.Harte, R. E., On quasinilpotents in rings, PanAm. Math. J. 1 (1991), 10–16.Google Scholar
12.Hartwig, R. E., Schur's theorem and the Drazin inverse, Pacific J. Math. 78 (1978), 133–138.CrossRefGoogle Scholar
13.Heuser, H. G., Functional Analysis (Wiley, New York, 1982).Google Scholar
14.King, C. F., A note on Drazin inverses, Pacific J. Math. 70 (1977), 383–390.CrossRefGoogle Scholar
15.Koliha, J. J., Isolated spectral points, Proc. Amer. Math. Soc, to appear.Google Scholar
16.Lay, D. C., Spectral properties of generalized inverses of linear operators, SIAM J. Appl. Math. 29 (1975), 103–109.CrossRefGoogle Scholar
17.Marek, I. and Žitný, K., Matrix Analysis for Applied Sciences, Vol. 2, Teubner-Texte zur Mathematik Band 84 (Teubner, Leipzig, 1986).Google Scholar
18.Nashed, M. Z., ed., Generalized Inverses and Applications (Academic Press, New York, 1976).Google Scholar
19.Nashed, M. Z. and Zhao, Y., The Drazin inverse for singular evolution equations and partial differential equations, World Sci. Ser. Appl. Anal. 1 (1992), 441–456.Google Scholar
20.Rothblum, U. G., A representation of the Drazin inverse and characterizations of the index, SIAM J. Appl. Math. 31 (1976), 646–648.CrossRefGoogle Scholar
21.Simeon, B., Führer, C. and Rentrop, P., The Drazin inverse in multibody system dynamics, Numer. Math. 64 (1993), 521–539.CrossRefGoogle Scholar
22.Taylor, A. E. and Lay, D. C., Introduction to functional analysis, 2nd edition (Wiley, New York, 1980).Google Scholar