The strongly irreducible operators in nest algebras |
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Authors: | You Qing Ji Chun Lan Jiang Zong Yao Wang |
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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 |
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Abstract: | An operatorT on
is called strongly irreducible ifT does not commute with any nontrivial idempotent operator. In this paper, we first show that each nest algebra (
) 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 (
).This project was partially supported by National Natural Science Foundation of China. |
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Keywords: | 47A05 |
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