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Joint m-quasihyponormal operators on a Hilbert space

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Abstract

In this paper, We introduce a new class of multivariable operators known as joint m-quasihyponormal tuple of operators. It is a naturel extension of joint normal and joint hyponormal tuples of operators. An m-tuple of operators \(\mathbf{S}=(S_1, \ldots ,S_m)\in {{\mathcal {B}}}({{\mathcal {H}}})^m\) is said to be joint m-quasihyponormal tuple if \(\mathbf{S}\) satisfying

$$\begin{aligned} \displaystyle \sum _{1\le l,\;k\;\le m}\big \langle S_k^*\big [S_k^*,\;\; S_l\big ]S_lu_k\;|\;u_l\big \rangle \ge 0, \end{aligned}$$

for each finite collections \((u_l)_{1\le l\le m}\in {{\mathcal {H}}}.\) Some properties of this class of multivariable operators are studied.

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at Jouf University for funding this work through research Grant no (DSR2020-05-3646). The authors express their sincere thanks to the reviewer for his/her comments on the paper.

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Authors and Affiliations

  1. Mathematics Department, College of Science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia

    Sid Ahmed Ould Ahmed Mahmoud & Hadi Obaid Alshammari

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  1. Sid Ahmed Ould Ahmed Mahmoud
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  2. Hadi Obaid Alshammari
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Correspondence to Sid Ahmed Ould Ahmed Mahmoud.

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Communicated by Hugo Woerdeman.

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Mahmoud, S.A.O.A., Alshammari, H.O. Joint m-quasihyponormal operators on a Hilbert space. Ann. Funct. Anal. 12, 42 (2021). https://doi.org/10.1007/s43034-021-00130-z

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