Continuity of the Drazin inverse II

J. Koliha; V. Rakočević

Studia Mathematica (1998)

  • Volume: 131, Issue: 2, page 167-177
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Koliha, J., and Rakočević, V.. "Continuity of the Drazin inverse II." Studia Mathematica 131.2 (1998): 167-177. <http://eudml.org/doc/216573>.

@article{Koliha1998,
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.},
author = {Koliha, J., Rakočević, V.},
journal = {Studia Mathematica},
keywords = {Banach algebra; bounded linear operator; generalized Drazin inverse; continuity of the Drazin inverse; continuity of the generalized Drazin inverse; Banach algebras},
language = {eng},
number = {2},
pages = {167-177},
title = {Continuity of the Drazin inverse II},
url = {http://eudml.org/doc/216573},
volume = {131},
year = {1998},
}

TY - JOUR
AU - Koliha, J.
AU - Rakočević, V.
TI - Continuity of the Drazin inverse II
JO - Studia Mathematica
PY - 1998
VL - 131
IS - 2
SP - 167
EP - 177
AB - 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.
LA - eng
KW - Banach algebra; bounded linear operator; generalized Drazin inverse; continuity of the Drazin inverse; continuity of the generalized Drazin inverse; Banach algebras
UR - http://eudml.org/doc/216573
ER -

References

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  1. [1] S. L. Campbell and C. D. Meyer, Continuity properties of the Drazin inverse, Linear Algebra Appl. 10 (1975), 77-83. Zbl0301.15004
  2. [2] S. L. Campbell and C. D. Meyer, Generalized Inverses of Linear Transformations, Pitman, London, 1979. Zbl0417.15002
  3. [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. [4] M. P. Drazin, Pseudo-inverse in associative rings and semigroups, Amer. Math. Monthly 65 (1958), 506-514. Zbl0083.02901
  5. [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. [6] R. E. Harte, Spectral projections, Irish Math. Soc. Newsletter 11 (1984), 10-15. Zbl0556.47001
  7. [7] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Springer, Berlin, 1980. 
  8. [8] C. F. King, A note on Drazin inverses, Pacific J. Math. 70 (1977), 383-390. Zbl0382.47001
  9. [9] J. J. Koliha, A generalized Drazin inverse, Glasgow Math. J. 38 (1996), 367-381. Zbl0897.47002
  10. [10] J. J. Koliha, Isolated spectral points, Proc. Amer. Math. Soc. 124 (1996), 3417-3424. Zbl0864.46028
  11. [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. [12] T. W. Palmer, Banach Algebras and the General Theory of *-Algebras, Vol. I, Encyclopedia Math. Appl. 49, Cambridge Univ. Press, Cambridge, 1994. Zbl0809.46052
  13. [13] V. Rakočević, Continuity of the Drazin inverse, J. Operator Theory, to appear. Zbl0990.47002
  14. [14] V. Rakočević, On the continuity of the Moore-Penrose inverse in Banach algebras, Facta Univ. (Niš) Ser. Math. Inform. 6 (1991), 133-138. Zbl0774.46026
  15. [15] C. E. Rickart, General Theory of Banach Algebras, Van Nostrand Reinhold, New York, 1960. Zbl0095.09702

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