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 τ(\(\mathcal{N}\)) 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 τ(\(\mathcal{N}\)).
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This project was partially supported by National Natural Science Foundation of China.
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Ji, Y.Q., Jiang, C.L. & Wang, Z.Y. The strongly irreducible operators in nest algebras. Integr equ oper theory 28, 28–44 (1997). https://doi.org/10.1007/BF01198794
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DOI: https://doi.org/10.1007/BF01198794