| Title:
|
On $(n,m)$-$A$-normal and $(n,m)$-$A$-quasinormal semi-Hilbertian space operators (English) |
| Author:
|
Al Mohammady, Samir |
| Author:
|
Ould Beinane, Sid Ahmed |
| Author:
|
Ould Ahmed Mahmoud, Sid Ahmed |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
147 |
| Issue:
|
2 |
| Year:
|
2022 |
| Pages:
|
169-186 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces, i.e. spaces generated by positive semi-definite sesquilinear forms. Let ${\mathcal H}$ be a Hilbert space and let $A$ be a positive bounded operator on ${\mathcal H}$. The semi-inner product $\langle h\mid k\rangle _A:=\langle Ah\mid k\rangle $, $h,k \in {\mathcal H}$, induces a semi-norm $\|{\cdot }\|_A$. This makes ${\mathcal H}$ into a semi-Hilbertian space. An operator $T\in {\mathcal B}_A({\mathcal H})$ is said to be $(n,m)$-$A$-normal if $[T^n,(T^{\sharp _A})^m]:=T^n(T^{\sharp _A})^m-(T^{\sharp _A})^mT^n=0$ for some positive integers $n$ and $m$. (English) |
| Keyword:
|
semi-Hilbertian space |
| Keyword:
|
$A$-normal operator |
| Keyword:
|
$(n,m)$-normal operator |
| Keyword:
|
$(n,m)$-quasinormal operator |
| MSC:
|
47B20 |
| MSC:
|
47B50 |
| MSC:
|
47B99 |
| MSC:
|
54E40 |
| idZBL:
|
Zbl 07547248 |
| idMR:
|
MR4407350 |
| DOI:
|
10.21136/MB.2021.0167-19 |
| . |
| Date available:
|
2022-04-14T13:40:38Z |
| Last updated:
|
2022-09-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150326 |
| . |
| Reference:
|
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