| 关于无限维线性系统在生成的紧扰动下的非指数稳定性 |
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| 引用本文： | 祝亭玉,胡燕,黄发伦.关于无限维线性系统在生成的紧扰动下的非指数稳定性[J].四川大学学报(自然科学版),2003,40(2):217-220. |
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| 作者姓名： | 祝亭玉 胡燕 黄发伦 |
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| 作者单位： | 四川大学数学学院,成都,610064 |
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| 基金项目： | The NSF of China |
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| 摘 要： | 分别证明了无限维自反Banach空间和无限维Hilbert空间中的反有界C0—群和C0—等距半群在生成的紧扰动下一定不具指数稳定性，因此推广和改进了Russell定理．
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| 关 键 词： | 非指数稳定性 Russell定理 Lebesgue－控制收敛定理 紧扰动 反有界C0－群 无限维线性系统 |
| 文章编号： | 0490-6756(2003)02-0217-04 |
Non-exponential Stability of Infinite-Dimensional Linear Systems under Generating Compact Perturbation |
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| ZHU Ting yu,HU Yan,HUANG Fa lun.Non-exponential Stability of Infinite-Dimensional Linear Systems under Generating Compact Perturbation[J].Journal of Sichuan University (Natural Science Edition),2003,40(2):217-220. |
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| Authors: | ZHU Ting yu HU Yan HUANG Fa lun |
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| Abstract: | The authors prove that an anti-bounded C0- group in infinite-dimensional reflexive Banach spaces is not exponentially stable under generating compact perturbation, and that a C0- isometric semigroup in infinite-dimensional Hilbert spaces has the same property. So the results have extended and improved Russell theorem. |
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| Keywords: | exponentially stable Russell theorem Lebesgue-dominated convergence theorem compact perturbation anti-bounded C0- group C0- isometric semigroup |
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