μ-Norm and Regularity.

In Treschev (Proc Steklov Math Inst 310:262–290, 2020) we introduce the concept of a μ -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 μ -norm. More precisely, we specify three classes of unitary operators for which the μ -norm generates a bistochastic operator. We plan to use the latter in the construction of quantum entropy. [ABSTRACT FROM AUTHOR]