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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The reduced minimum modulus of Drazin inverses of linear operators on Hilbert spaces


Authors: Chun-Yuan Deng and Hong-Ke Du
Journal: Proc. Amer. Math. Soc. 134 (2006), 3309-3317
MSC (2000): Primary 47A05, 46C07, 15A09
Published electronically: May 12, 2006
MathSciNet review: 2231916
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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.


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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: http://dx.doi.org/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
Published electronically: May 12, 2006
Additional Notes: This research was partially supported by the National Natural Science Foundation of China (10571113).
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.