| Title:
|
On the range of some elementary operators (English) |
| Author:
|
El Mouadine, Hamza |
| Author:
|
Faouzi, Abdelkhalek |
| Author:
|
Bouhafsi, Youssef |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
65 |
| Issue:
|
1 |
| Year:
|
2024 |
| Pages:
|
53-62 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $L(H)$ denote the algebra of all bounded linear operators on a complex infinite dimensional Hilbert space $H$. For $A,B\in L(H)$, the generalized derivation $\delta_{A,B}$ and the multiplication operator $M_{A,B}$ are defined on $L(H)$ by $\delta_{A,B}(X)=AX-XB$ and $M_{A,B}(X)=AXB$. In this paper, we give a characterization of bounded operators $A$ and $B$ such that the range of $M_{A,B}$ is closed. We present some sufficient conditions for $\delta_{A,B}$ to have closed range. Some related results are also given. (English) |
| Keyword:
|
generalized derivation |
| Keyword:
|
elementary operator |
| Keyword:
|
generalized inverse |
| Keyword:
|
Kato spectrum |
| MSC:
|
47A16 |
| MSC:
|
47A30 |
| MSC:
|
47B07 |
| MSC:
|
47B20 |
| MSC:
|
47B47 |
| idZBL:
|
Zbl 08063786 |
| idMR:
|
MR4899030 |
| DOI:
|
10.14712/1213-7243.2025.004 |
| . |
| Date available:
|
2025-04-24T07:48:50Z |
| Last updated:
|
2026-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152944 |
| . |
| 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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| . |
