Jointly A-hyponormal m-tuple of commuting operators and related results
In this paper, we aim to investigate the class of jointly hyponormal operators related to a positive operator $ A $ on a complex Hilbert space $ \mathcal{X} $, which is called jointly $ A $-hyponormal. This notion was first introduced by Guesba et al. in [Linear and Multilinear Algebra, 69(15), 2888...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-10-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241464?viewType=HTML |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this paper, we aim to investigate the class of jointly hyponormal operators related to a positive operator $ A $ on a complex Hilbert space $ \mathcal{X} $, which is called jointly $ A $-hyponormal. This notion was first introduced by Guesba et al. in [Linear and Multilinear Algebra, 69(15), 2888–2907] for $ m $-tuples of operators that admit adjoint operators with respect to $ A $. Mainly, we prove that if $ \mathbf{B} = (B_1, \cdots, B_m) $ is a jointly $ A $-hyponormal $ m $-tuple of commuting operators, then $ \mathbf{B} $ is jointly $ A $-normaloid. This result allows us to establish, for a particular case when $ A $ is the identity operator, a sharp bound for the distance between two jointly hyponormal $ m $-tuples of operators, expressed in terms of the difference between their Taylor spectra. We also aim to introduce and investigate the class of spherically $ A $-$ p $-hyponormal operators with $ 0 < p < 1 $. Additionally, we study the tensor product of specific classes of multivariable operators in semi-Hilbert spaces. |
|---|---|
| ISSN: | 2473-6988 |