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

DOI:
https://doi.org/10.1090/S0002-9939-06-08377-8

Published electronically:
May 12, 2006

MathSciNet review:
2231916

Full-text PDF

Abstract | References | Similar Articles | 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.

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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:
https://doi.org/10.1090/S0002-9939-06-08377-8

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.