Finite rank operators in Jacobson radical ${\scr R}\sb{{\scr N}\otimes{\scr M}}$

Title:

Finite rank operators in Jacobson radical ${\scr R}\sb{{\scr N}\otimes{\scr M}}$

Creator:

Zhe, Dong

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:824a26fd-b6df-4d69-8e1b-cd31e4827831
uuid:824a26fd-b6df-4d69-8e1b-cd31e4827831

Subject:

Jacobson radical and finite rank operator

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper we investigate finite rank operators in the Jacobson radical $\mathcal R_{\mathcal N\otimes \mathcal M}$ of $\mathop {\mathrm Alg}(\mathcal N\otimes \mathcal M)$, where $\mathcal N$, $\mathcal M$ are nests. Based on the concrete characterizations of rank one operators in $\mathop {\mathrm Alg}(\mathcal N\otimes \mathcal M)$ 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 $\mathop {\mathrm Alg}({\mathcal N\otimes \mathcal M})$ if and only if at least one of $\mathcal N$, $\mathcal M$ is continuous.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

287-298

Source:

Czechoslovak Mathematical Journal | 2006 Volume:56 | Number:2

Harvested from:

CDK

Metadata only:

false