$μ$-norm and regularity

In \cite{Tre_PSI20} 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 \cite{Tre_PSI20} 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.

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