Index of B-Fredholm operators and generalization of a Weyl theorem
Index of B-Fredholm operators and generalization of a Weyl theorem
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DOI：
10.1090/s0002-9939-01-06291-8
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
M. Berkani
中科院分区：
文献类型：
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作者：
M. Berkani
本文的目的是证明：如果S和T是作用在Banach空间X上的交换B-Fredholm算子，则ST是B-Fredholm算子且ind（ST）= ind（S）+ind（T），其中ind表示指数.此外，若T是B-Fredholm算子，F是有限秩算子，则T + F是B-Fredholm算子，且ind（T + F）= ind（T）.我们还证明了，如果0在T的谱中是孤立的，则T是指数为0的B-Fredholm算子当且仅当T是Drazin可逆的.对于Hilbert空间H上的正规有界线性算子T，我们得到了经典Weyl定理的一个推广.
The aim of this paper is to show that if S and T are commuting B-Fredholm operators acting on a Banach space X, then ST is a B-Fredholm operator and ind(ST) = ind(S) + ind(T), where ind means the index. Moreover if T is a B-Fredholm operator and F is a finite rank operator, then T + F is a B-Fredholm operator and ind(T + F) = ind(T). We also show that if 0 is isolated in the spectrum of T, then T is a B-Fredholm operator of index 0 if and only if T is Drazin invertible. In the case of a normal bounded linear operator T acting on a Hilbert space H, we obtain a generalization of a classical Weyl theorem.