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The strongly irreducible operators in nest algebras
Authors:You Qing Ji  Chun Lan Jiang  Zong Yao Wang
Institution:(1) Department of Mathematics, Jilin University, 130023 Changchun, Peoples Republic of China;(2) Department of Mathematics, East China University of Science and Technology, 200237 Shanghai, Peoples Republic of China
Abstract:An operatorT on 
$$\mathcal{H}$$
is called strongly irreducible ifT does not commute with any nontrivial idempotent operator. In this paper, we first show that each nest algebra tau( 
$$\mathcal{N}$$
) has strongly irreducible operators. Secondly, we obtain a characterization of operators which can be uniquely written as a direct sum of finitely many strongly irreducible operators. Finally, we characterize the strongly irreducibility of operators in a nest algebra tau( 
$$\mathcal{N}$$
).This project was partially supported by National Natural Science Foundation of China.
Keywords:47A05
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