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The reduced minimum modulus of Drazin inverses of linear operators on Hilbert spaces
Author(s):
Chun-Yuan
Deng;
Hong-Ke
Du
Journal:
Proc. Amer. Math. Soc.
134
(2006),
3309-3317.
MSC (2000):
Primary 47A05, 46C07, 15A09
Posted:
May 12, 2006
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Additional information
Abstract:
In this article, we study the reduced minimum modulus of the Drazin inverse of an operator on a Hilbert space and give lower and upper bounds of the reduced minimum modulus of an operator and its Drazin inverse, respectively. Using these results, we obtain a characterization of the continuity of Drazin inverses of operators on a Hilbert space.
References:
-
- 1.
- A. Ben-Israel, T. N. E. Greville, Generalized Inverses: Theory and Applications, 2nd Edition, Springer-Verlag, New York, 2003. MR 1987382 (2004b:15008)
- 2.
- S. L. Campbell, Recent applications of generalized inverses, Pitman, London, 1982. MR 0666720 (83h:65010)
- 3.
- J. Ding, L. J. Huang, Perturbation of Generalized Inverses of Linear Operators in Hilbert Spaces, Journal of Mathematical Analysis and Applications, 198(1996), 506-515. MR 1376277 (97i:47017)
- 4.
- D. S. Djordjevic, Y. Wei, Additive results for the generalized Drazin inverse, J. Austral Math. Soc., 73(2002), 115-125. MR 1916312 (2003e:47002)
- 5.
- H. Du, C. Deng, A new characterization of gaps between two subspaces, Proceedings of the American Mathematical Society, 133(2005), 3065-3070. MR 2159786
- 6.
- H. Du, C. Deng, The representation and characterization of Drazin inverses of operators on a Hilbert space, Linear Algebra and its Applications, 407(2005), 117-124. MR 2161918 (2006d:47001)
- 7.
- R. E. Hartwig, Gworong Wang, Yimin Wei, Some additive results on Drazin inverses, Linear Algebra and its Applications, 322(2001), 207-217. MR 1804521 (2001k:15004)
- 8.
- D. T. Kato, Perturbation theory for linear operators, Springer, New York, 1966. MR 0203473 (34:3324)
- 9.
- A. E. Taylar, D. C. Lay, Introduction to functional analysis 2nd Edition, John Wiley
 Sons, New York, Chichester, Brisbane, Toronto, 1980. MR 0564653 (81b:46001) - 10.
- G. Wang, Y. Wei, S. Qiao, Generalized inverses: Theory and Computions, Science Press, Beijing, New York, 2004.
- 11.
- Yimin Wei, Guoliang Chen, Perturbation of least squares problem in Hilbert spaces, Applied Mathematics and Computation, 121(2001), 177-183. MR 1830868 (2002b:47022)
- 12.
- Yimin Wei, Sanzheng Qiao, The representation and approximation of the Drazin inverse of a linear operator in Hilbert space, Applied Mathematics and Computation, 138(2003), 77-89. MR 1950346 (2003j:47001)
- 13.
- Yimin Wei, A characterization and representation of the generalized inverse
 and its applications, Linear Algebra and its Applications, 280(1998), 87-96. MR 1645022 (99g:15006) - 14.
- Yimin Wei, A characterization and representation of the Drazin inverse, SIAM J. Matrix Anal. Appl., 17(1996), 744-747. MR 1410699 (97k:15008)
- 15.
- Liping Zhang, A characterization of the Drazin inverse, Linear Algebra and its Applications, 335(2001), 183-188. MR 1850823 (2002f:15007)
- 16.
- Chao Zhu, Jing Cai, Guo-liang Chen, Perturbation analysis for the reduced minimum modulus of bounded linear operator in Banach spaces, Applied Mathematics and Computation, 145(2003), 13-21. MR 2005984 (2004g:47005)
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Additional Information:
Chun-Yuan
Deng
Affiliation:
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, People's Republic of China
Email:
cy-deng@263.net
Hong-Ke
Du
Affiliation:
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, People's Republic of China
Email:
hkdu@snnu.edu.cn
DOI:
10.1090/S0002-9939-06-08377-8
PII:
S 0002-9939(06)08377-8
Keywords:
Drazin inverse,
reduced minimum modulus,
gap between two subspaces
Received by editor(s):
May 11, 2005
Received by editor(s) in revised form:
May 31, 2005
Posted:
May 12, 2006
Additional Notes:
This research was partially supported by the National Natural Science Foundation of China (10571113).
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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