| Title:
|
On the range-kernel orthogonality of elementary operators (English) |
| Author:
|
Bouali, Said |
| Author:
|
Bouhafsi, Youssef |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
140 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
261-269 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $L(H)$ denote the algebra of operators on a complex infinite dimensional Hilbert space $H$. For $A, B\in L(H)$, the generalized derivation $\delta _{A,B}$ and the elementary operator $\Delta _{A,B}$ are defined by $\delta _{A,B}(X)=AX-XB$ and $\Delta _{A,B}(X)=AXB-X$ for all $X\in L(H)$. In this paper, we exhibit pairs $(A,B)$ of operators such that the range-kernel orthogonality of $\delta _{A,B}$ holds for the usual operator norm. We generalize some recent results. We also establish some theorems on the orthogonality of the range and the kernel of $\Delta _{A,B}$ with respect to the wider class of unitarily invariant norms on $L(H)$. (English) |
| Keyword:
|
derivation |
| Keyword:
|
elementary operator |
| Keyword:
|
orthogonality |
| Keyword:
|
unitarily invariant norm |
| Keyword:
|
cyclic subnormal operator |
| Keyword:
|
Fuglede-Putnam property |
| MSC:
|
47A30 |
| MSC:
|
47A63 |
| MSC:
|
47B10 |
| MSC:
|
47B15 |
| MSC:
|
47B20 |
| MSC:
|
47B47 |
| idZBL:
|
Zbl 06486938 |
| idMR:
|
MR3397256 |
| DOI:
|
10.21136/MB.2015.144393 |
| . |
| Date available:
|
2015-09-03T10:47:52Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144393 |
| . |
| 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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| . |
