In Treschev (Proc Steklov Math Inst 310:262–290, 2020) we introduce the concept of a \(\mu \)-norm for a bounded operator in a Hilbert space. The main motivation is the extension of the measure entropy to the case of quantum systems. In this paper we recall the basic results from Treschev (2020) and present further results on the \(\mu \)-norm. More precisely, we specify three classes of unitary operators for which the \(\mu \)-norm generates a bistochastic operator. We plan to use the latter in the construction of quantum entropy.

中文翻译：

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$$ \ mu $$μ-规范和规律性

在Treschev（Proc Steklov Math Inst 310：262–290，2020）中，我们引入了Hilbert空间中有界算子的\（\ mu \）-范数的概念。其主要动机是将量度熵扩展到量子系统的情况。在本文中，我们回顾了Treschev（2020）的基本结果，并给出了\（\ mu \）-范数的进一步结果。更准确地说，我们指定\（\ mu \）- norm为其生成双随机算子的三类of算子。我们计划在量子熵的构造中使用后者。