Lack of uniformly exponential stabilization for isometric $C_0$-semigroups under compact perturbation of the generators in Banach spaces
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- by Faming Guo, Ke Guo and Chaolun Zhang PDF
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Addendum: Proc. Amer. Math. Soc. 137 (2009), 2809-2812.
Abstract:
This paper is concerned with non-uniformly exponential stabilization for infinite-dimensional linear systems under compact feedback in Banach spaces. We prove that a compact perturbation of the generator of an isometric $C_0$-semigroup cannot generate a uniformly exponentially stable $C_0$-semigroup in a Banach space. Finally, examples are provided to illustrate our result.References
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Additional Information
- Faming Guo
- Affiliation: Department of Applied Mathematics, College of Information Management, Chengdu University of Technology, Chengdu, 610059, People’s Republic of China
- Email: guofm@uestc.edu.cn
- Ke Guo
- Affiliation: Department of Applied Mathematics, College of Information Management, Chengdu University of Technology, Chengdu, 610059, People’s Republic of China
- Chaolun Zhang
- Affiliation: Institute of Applied Mathematics, Xihua University, Chengdu, 610039, People’s Republic of China
- Received by editor(s): January 14, 2006
- Received by editor(s) in revised form: February 23, 2006
- Published electronically: February 2, 2007
- Additional Notes: This research was supported by the Postdoctoral Science Foundation of China.
- Communicated by: Joseph A. Ball
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1881-1887
- MSC (2000): Primary 47A50, 47A55
- DOI: https://doi.org/10.1090/S0002-9939-07-08698-4
- MathSciNet review: 2286100