ArticleOriginal scientific text

Title

Continuity of the Drazin inverse II

Authors 1, 2

Affiliations

  1. Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3052, Australia
  2. Department of Mathematics, Faculty of Philosophy, University of Niš, 18000 Niš, Yugoslavia - Serbia

Abstract

We study the continuity of the generalized Drazin inverse for elements of Banach algebras and bounded linear operators on Banach spaces. This work extends the results obtained by the second author on the conventional Drazin inverse.

Keywords

Banach algebra, bounded linear operator, generalized Drazin inverse, continuity of the Drazin inverse

Bibliography

  1. S. L. Campbell and C. D. Meyer, Continuity properties of the Drazin inverse, Linear Algebra Appl. 10 (1975), 77-83.
  2. S. L. Campbell and C. D. Meyer, Generalized Inverses of Linear Transformations, Pitman, London, 1979.
  3. S. R. Caradus, Generalized inverses and operator theory, Queen's Papers in Pure and Appl. Math. 50, Queen's Univ., Kingston, Ont., 1978.
  4. M. P. Drazin, Pseudo-inverse in associative rings and semigroups, Amer. Math. Monthly 65 (1958), 506-514.
  5. I. C. Gohberg and A. S. Markus, Two theorems on the opening between subspaces of a Banach space, Uspekhi Mat. Nauk 14 (1959), no. 5, 135-140 (in Russian).
  6. R. E. Harte, Spectral projections, Irish Math. Soc. Newsletter 11 (1984), 10-15.
  7. T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Springer, Berlin, 1980.
  8. C. F. King, A note on Drazin inverses, Pacific J. Math. 70 (1977), 383-390.
  9. J. J. Koliha, A generalized Drazin inverse, Glasgow Math. J. 38 (1996), 367-381.
  10. J. J. Koliha, Isolated spectral points, Proc. Amer. Math. Soc. 124 (1996), 3417-3424.
  11. A. S. Markus, On some properties of linear operators connected with the notion of the gap, Uchen. Zap. Kishinev. Gos. Univ. 39 (1959), 265-272 (in Russian).
  12. T. W. Palmer, Banach Algebras and the General Theory of *-Algebras, Vol. I, Encyclopedia Math. Appl. 49, Cambridge Univ. Press, Cambridge, 1994.
  13. V. Rakočević, Continuity of the Drazin inverse, J. Operator Theory, to appear.
  14. V. Rakočević, On the continuity of the Moore-Penrose inverse in Banach algebras, Facta Univ. (Niš) Ser. Math. Inform. 6 (1991), 133-138.
  15. C. E. Rickart, General Theory of Banach Algebras, Van Nostrand Reinhold, New York, 1960.
Pages:
167-177
Main language of publication
English
Received
1997-10-29
Accepted
1998-03-10
Published
1998
Exact and natural sciences