| On the Equivalence and Generalized of Weyl Theorem Weyl Theorem |
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| 作者姓名： | M. BERKANI |
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| 作者单位： | Groupe d＇Analyse et Tháorie des Opdrateurs （G.A.T.O.）,Dápartement de Mathématiques, Université Mohammed I, Faculté des Sciences,Oujda 60000, Morocco |
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| 基金项目： | Supported by Protars D11/16 and Project P/201/03 （Morocco-Spain（AECI）） |
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| 摘 要： | We know that an operator T acting on a Banach space satisfying generalized Weyl＇s theorem also satisfies Weyl＇s theorem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl＇s theorem, then it also satisfies generalized Weyl＇s theorem. We give also a sinlilar result for the equivalence of a-Weyl＇s theorem and generalized a-Weyl＇s theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators.
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| 关 键 词： | B-Fredholm算子 Weyl定理 广义Weyl定理 a-Weyl定理 |
| 收稿时间： | 12 October 2004 |
| 修稿时间： | 2004-10-122005-03-01 |
On the Equivalence of Weyl Theorem and Generalized Weyl Theorem |
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| M. BERKANI.On the Equivalence and Generalized of Weyl Theorem Weyl Theorem[J].Acta Mathematica Sinica,2007,23(1):103-110. |
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| Authors: | M Berkani |
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| Institution: | (1) Groupe d’Analyse et Théorie des Opérateurs (G.A.T.O.), Département de Mathématiques, Université Mohammed I, Faculté des Sciences, Oujda 60000, Morocco |
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| Abstract: | We know that an operator T acting on a Banach space satisfying generalized Weyl’s theorem also satisfies Weyl’s theorem. Conversely we show that if
all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl’s theorem, then it also satisfies generalized Weyl’s theorem. We give also a similar result for the equivalence
of a–Weyl’s theorem and generalized a–Weyl’s theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators.
Supported by Protars D11/16 and Project P/201/03 (Morocco–Spain(AECI)) |
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| Keywords: | B– Fredholm operator Weyl’ s theorem generalized Weyl’ s theorem a– Weyl’ s theorem generalized a– Weyl’ s theorem poles |
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