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Commuting Tuples of Normal Operators in Hilbert Spaces

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Abstract

In this paper we aim to study the tensor product and the tensor sum of two jointly-normal operators. Mainly, an alternative proof is given for the result of Chō and Takaguchi (Pac J Math 95(1):27–35, 1981) asserting that: if \(\mathbf {T}\) is jointly-normal, then \(r(\mathbf {T})=\Vert \mathbf {T}\Vert =\omega (\mathbf {T})\), where \(r(\mathbf {T})\), \(\omega (\mathbf {T})\) and \(\Vert \mathbf {T}\Vert \) denote respectively the joint spectral radius, the joint numerical radius and the joint norm of an operator tuple \(\mathbf {T}\). It seems that this new method allows to handle more general situations, namely the operators acting on semi-hilbertian spaces.

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Acknowledgements

The second author would like to express his cordial gratitude to professor Thierry Gallouët (Aix-Marseille University) for valuable advice and suggestions in the proof of Theorem 4.3.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, B.P. 1171, 3000, Sfax, Tunisia

    Hamadi Baklouti & Kais Feki

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  1. Hamadi Baklouti
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  2. Kais Feki
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Correspondence to Kais Feki.

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Communicated by Victor Vinnikov.

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Baklouti, H., Feki, K. Commuting Tuples of Normal Operators in Hilbert Spaces. Complex Anal. Oper. Theory 14, 56 (2020). https://doi.org/10.1007/s11785-020-01013-2

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