Mbekhta’s subspaces and a spectral theory of compact operators
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- by Weibang Gong and Libin Wang
- Proc. Amer. Math. Soc. 131 (2003), 587-592
- DOI: https://doi.org/10.1090/S0002-9939-02-06639-X
- Published electronically: July 17, 2002
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Abstract:
Let $A$ be an operator on an infinite-dimensional complex Banach space. By means of Mbekhta’s subspaces $H_{0}(A)$ and $K(A)$, we give a spectral theory of compact operators. The main results are: Let $A$ be compact. $1$. The following assertions are all equivalent: (1) 0 is an isolated point in the spectrum of $A;$ (2) $K(A)$ is closed; (3) $K(A)$ is of finite dimension; (4) $K(A^{\ast })$ is closed; (5) $K(A^{\ast })$ is of finite dimension; $2$. sufficient conditions for $0$ to be an isolated point in $\sigma (A)$; $3$. sufficient and necessary conditions for $0$ to be a pole of the resolvent of $A$.References
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Bibliographic Information
- Weibang Gong
- Affiliation: Department of Mathematics, Qufu Normal University, Qufu, Shandong, 273165, People’s Republic of China
- Email: gongwb@ji-public.sd.cninfo.net
- Libin Wang
- Affiliation: Department of Mathematics, Qufu Normal University, Qufu, Shandong, 273165, People’s Republic of China
- Received by editor(s): April 19, 2001
- Received by editor(s) in revised form: October 2, 2001
- Published electronically: July 17, 2002
- Additional Notes: This paper is project 19871048 supported by the NSFC
- Communicated by: Joseph A. Ball
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 587-592
- MSC (2000): Primary 47A10, 47A11
- DOI: https://doi.org/10.1090/S0002-9939-02-06639-X
- MathSciNet review: 1933350