\(\mu\)-norm and regularity. (English) Zbl 1471.81012
Summary: In the author [Proc. Steklov Inst. Math. 310, 262–290 (2020; Zbl 1453.81020); translation from Tr. Mat. Inst. Steklova 310, 280–308 (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 the author [loc. cit.] 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.
MSC:
| 81P17 | Quantum entropies |
| 47A30 | Norms (inequalities, more than one norm, etc.) of linear operators |
| 47B40 | Spectral operators, decomposable operators, well-bounded operators, etc. |
Citations:
Zbl 1453.81020References:
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