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Lack of uniformly exponential stabilization for isometric  -semigroups under compact perturbation of the generators in Banach spaces
Author(s):
Faming
Guo;
Ke
Guo;
Chaolun
Zhang
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1881-1887.
MSC (2000):
Primary 47A50, 47A55
Posted:
February 2, 2007
Addenda:
Proc. Amer. Math. Soc.
137 (2009),
2809-2812
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Additional information
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  -semigroup cannot generate a uniformly exponentially stable  -semigroup in a Banach space. Finally, examples are provided to illustrate our result.
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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
DOI:
10.1090/S0002-9939-07-08698-4
PII:
S 0002-9939(07)08698-4
Keywords:
Compact perturbation,
isometric $C_0$-semigroup,
exponential stability.
Received by editor(s):
January 14, 2006
Received by editor(s) in revised form:
February 23, 2006
Posted:
February 2, 2007
Additional Notes:
This research was supported by the Postdoctoral Science Foundation of China.
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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