| Title:
|
A remark on the range of elementary operators (English) |
| Author:
|
Bouali, Said |
| Author:
|
Bouhafsi, Youssef |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
1065-1074 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $L(H)$ denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space $H$ into itself. Given $A\in L(H)$, we define the elementary operator $\Delta _A\colon L(H)\longrightarrow L(H)$ by $\Delta _A(X)=AXA-X$. In this paper we study the class of operators $A\in L(H)$ which have the following property: $ATA=T$ implies $AT^{\ast }A=T^{\ast }$ for all trace class operators $T\in C_1(H)$. Such operators are termed generalized quasi-adjoints. The main result is the equivalence between this character and the fact that the ultraweak closure of the range of $\Delta _A$ is closed under taking adjoints. We give a characterization and some basic results concerning generalized quasi-adjoints operators. (English) |
| Keyword:
|
elementary operators |
| Keyword:
|
ultraweak closure |
| Keyword:
|
weak closure |
| Keyword:
|
quasi-adjoint operator |
| MSC:
|
47A30 |
| MSC:
|
47B10 |
| MSC:
|
47B20 |
| MSC:
|
47B47 |
| idZBL:
|
Zbl 1220.47049 |
| idMR:
|
MR2738968 |
| . |
| Date available:
|
2010-11-20T13:59:13Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140805 |
| . |
| Reference:
|
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