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.

中文翻译：

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Hilbert空间中正规算子的通勤元组

本文旨在研究两个联合正则算子的张量积和张量和。主要是，对Chō和Takaguchi的结果给出了另一种证明（Pac J Math 95（1）：27-35，1981）断言：如果\（\ mathbf {T} \）是联合正态的，则\（ r（\ mathbf {T}）= \ Vert \ mathbf {T} \ Vert = \ omega（\ mathbf {T}）\），其中\（r（\ mathbf {T}）\），\（\ omega（ \ mathbf {T}）\）和\（\ Vert \ mathbf {T} \ Vert \）分别表示运算符元组的联合谱半径，联合数值半径和联合范数\（\ mathbf {T} \）。看来，这种新方法可以处理更一般的情况，即作用于半希尔伯特空间上的算子。