Finite rank operators in Jacobson radical \mathcal{R}_{\mathcal{N} \otimes \mathcal{M}}期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Finite rank operators in Jacobson radical \mathcal{R}_{\mathcal{N} \otimes \mathcal{M}}

Authors:	Dong Zhe

Institution:	(1) Department of Mathematics, Zhejiang University, Hangzhou, 310027, P.R. China

Abstract:	In this paper we investigate finite rank operators in the Jacobson radical $\mathcal{R}_{\mathcal{N} \otimes \mathcal{M}}$ of Alg( $\mathcal{N} \otimes \mathcal{M}$ ), where $\mathcal{N}, \mathcal{M}$ are nests. Based on the concrete characterizations of rank one operators in Alg( $\mathcal{N} \otimes \mathcal{M}$ ) and $\mathcal{R}_{\mathcal{N} \otimes \mathcal{M}}$ , we obtain that each finite rank operator in $\mathcal{R}_{\mathcal{N} \otimes \mathcal{M}}$ can be written as a finite sum of rank one operators in $\mathcal{R}_{\mathcal{N} \otimes \mathcal{M}}$ and the weak closure of $\mathcal{R}_{\mathcal{N} \otimes \mathcal{M}}$ equals Alg( $\mathcal{N} \otimes \mathcal{M}$ ) if and only if at least one of $\mathcal{N}, \mathcal{M}$ is continuous.

Keywords:	Jacobson radical finite rank operator
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