| Title:
|
Finite rank operators in Jacobson radical ${\scr R}\sb{{\scr N}\otimes{\scr M}}$ (English) |
| Author:
|
Zhe, Dong |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
287-298 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Jacobson radical |
| Keyword:
|
finite rank operator |
| MSC:
|
47L35 |
| MSC:
|
47L75 |
| idZBL:
|
Zbl 1164.47398 |
| idMR:
|
MR2291737 |
| . |
| Date available:
|
2009-09-24T11:33:07Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128067 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
