Quasi-entropies for states of a von Neumann algebra
The relative entropy functional of Araki is generalized. Let M be a von Neumann algebra with normal states \(\phi\) and \(\omega\). Our quasi-entropy \(S^ k_ f(\phi,\omega)\) depends on two parameters \(k\in M\) and f: [0,\(\infty)\to {\mathbb{R}}\). The counterpart of the quasi-entropy in classical information theory is the f-divergence of Csiszár. In the paper Lieb's concavity is recaptured in Kosaki's form. Continuity and monotonity theorems are discussed. The main technique is the application of the theory of operator monotone functions.
scientific article; zbMATH DE number 3979789