On $ (n_1, \cdots, n_m) $-hyponormal tuples of Hilbert space operators
This paper introduces a new class of multivariable operators called $ (n_1, \cdots, n_m) $-hyponormal tuples, which combine joint normal and joint hyponormal operators. A tuple of operators $ \mathcal{Q} = (\mathcal{Q}_1, \; \cdots, \mathcal{Q}_m) $ is said to be an $ (n_1, \cdots, n_m) $-hyponormal...
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AIMS Press
2024-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241349?viewType=HTML |
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| author | Sid Ahmed Ould Beinane Sid Ahmed Ould Ahmed Mahmoud |
| author_facet | Sid Ahmed Ould Beinane Sid Ahmed Ould Ahmed Mahmoud |
| author_sort | Sid Ahmed Ould Beinane |
| collection | DOAJ |
| description | This paper introduces a new class of multivariable operators called $ (n_1, \cdots, n_m) $-hyponormal tuples, which combine joint normal and joint hyponormal operators. A tuple of operators $ \mathcal{Q} = (\mathcal{Q}_1, \; \cdots, \mathcal{Q}_m) $ is said to be an $ (n_1, \cdots, n_m) $-hyponormal tuple for some $ (n_1, \cdots, n_m)\in \mathbb{N}^m $ if</p><p class="disp_formula">$ \sum\limits_{1\leq k,\;l\leq m}\big\langle[\mathcal{Q}_k^{*n_k}, \;\mathcal{Q}_l^{n_l}]\omega_k\mid \omega_l\big\rangle\geq 0, \quad \forall\; (\omega_k)_{1\leq k\leq m}\in {\mathcal K}^m. $</p><p>We show several properties of this class that correspond to the properties of joint hyponormal operators. |
| format | Article |
| id | doaj-art-d47e015ee4774bb09313927eb1b4dbbf |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-d47e015ee4774bb09313927eb1b4dbbf2025-08-20T02:08:44ZengAIMS PressAIMS Mathematics2473-69882024-09-01910277842779610.3934/math.20241349On $ (n_1, \cdots, n_m) $-hyponormal tuples of Hilbert space operatorsSid Ahmed Ould Beinane 0Sid Ahmed Ould Ahmed Mahmoud1Mathematics Department, College of Science, Jouf University, Sakaka, P. O. Box 2014, Saudi ArabiaMathematics Department, College of Science, Jouf University, Sakaka, P. O. Box 2014, Saudi ArabiaThis paper introduces a new class of multivariable operators called $ (n_1, \cdots, n_m) $-hyponormal tuples, which combine joint normal and joint hyponormal operators. A tuple of operators $ \mathcal{Q} = (\mathcal{Q}_1, \; \cdots, \mathcal{Q}_m) $ is said to be an $ (n_1, \cdots, n_m) $-hyponormal tuple for some $ (n_1, \cdots, n_m)\in \mathbb{N}^m $ if</p><p class="disp_formula">$ \sum\limits_{1\leq k,\;l\leq m}\big\langle[\mathcal{Q}_k^{*n_k}, \;\mathcal{Q}_l^{n_l}]\omega_k\mid \omega_l\big\rangle\geq 0, \quad \forall\; (\omega_k)_{1\leq k\leq m}\in {\mathcal K}^m. $</p><p>We show several properties of this class that correspond to the properties of joint hyponormal operators.https://www.aimspress.com/article/doi/10.3934/math.20241349?viewType=HTMLhilbert spacenormal operatorn-hyponormal operatorcommuting tuple of operators |
| spellingShingle | Sid Ahmed Ould Beinane Sid Ahmed Ould Ahmed Mahmoud On $ (n_1, \cdots, n_m) $-hyponormal tuples of Hilbert space operators AIMS Mathematics hilbert space normal operator n-hyponormal operator commuting tuple of operators |
| title | On $ (n_1, \cdots, n_m) $-hyponormal tuples of Hilbert space operators |
| title_full | On $ (n_1, \cdots, n_m) $-hyponormal tuples of Hilbert space operators |
| title_fullStr | On $ (n_1, \cdots, n_m) $-hyponormal tuples of Hilbert space operators |
| title_full_unstemmed | On $ (n_1, \cdots, n_m) $-hyponormal tuples of Hilbert space operators |
| title_short | On $ (n_1, \cdots, n_m) $-hyponormal tuples of Hilbert space operators |
| title_sort | on n 1 cdots n m hyponormal tuples of hilbert space operators |
| topic | hilbert space normal operator n-hyponormal operator commuting tuple of operators |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241349?viewType=HTML |
| work_keys_str_mv | AT sidahmedouldbeinane onn1cdotsnmhyponormaltuplesofhilbertspaceoperators AT sidahmedouldahmedmahmoud onn1cdotsnmhyponormaltuplesofhilbertspaceoperators |