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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-09-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241349?viewType=HTML |
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| Summary: | 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. |
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| ISSN: | 2473-6988 |