Our aim in this paper is to prove the equality between two kinds of joint operator norms in the case of doubly commuting tuples of hyponormal operators on Hilbert spaces. Moreover, a sharp bound for the distance between two doubly commuting tuples of hyponormal operators in terms of the distance between their Harte spectra is proved.

中文翻译：

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关于 Hilbert 空间上次正规算子的双通勤元组的注记

我们在本文中的目的是证明在 Hilbert 空间上次正规算子双交换元组的情况下两种联合算子范数之间的相等性。此外，证明了就其 Harte 谱之间的距离而言，次正规算子的两个双交换元组之间的距离存在尖锐界限。