The strongly irreducible operators in nest algebras

Springer Science and Business Media LLC - Tập 28 - Trang 28-44 - 1997
You Qing Ji1, Chun Lan Jiang1, Zong Yao Wang2
1Department of Mathematics, Jilin University, Changchun, Peoples Republic of China
2Department of Mathematics, East China University of Science and Technology, Shanghai, Peoples Republic of China

Tóm tắt

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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Springer Science and Business Media LLC

Tập 28

28-44

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