A Note on the Browder's and Weyl's Theorem

被引：6
作者：
Amouch, M. [1 ]
Zguitti, H. [2 ]
机构：
[1] Fac Sci Semlalia, Dept Math, Marrakech, Morocco
[2] Fac Sci Rabat, Dept Math, Rabat, Morocco
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2008年 / 24卷 / 12期
关键词：
Weyl's theorem; generalized Weyl's theorem; Browder's theorem; generalized Browder's theorem; single-valued extension property;
D O I：
10.1007/s10114-008-6633-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let T be a Banach space operator, E(T) be the set of all isolated eigenvalues of T and pi(T) be the set of all poles of T. In this work, we show that Browder's theorem for T is equivalent to the localized single-valued extension property at all complex numbers lambda in the complement of the Weyl spectrum of T, and we give some characterization of Weyl's theorem for operator satisfying E(T) = pi(T). An application is also given.
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页码：2015 / 2020
页数：6
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