The f_0-divergence defined via Jordan decomposition integrals coincides with Araki's relative entropy on arbitrary von Neumann algebras, extending Frenkel's finite-dimensional formula.
Pedersen,C ∗-Algebras and Their Automorphism Groups, Pure and Applied Mathematics, Academic Press (2018), DOI
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Integral representations of $f$-divergences for general von Neumann algebras
The f_0-divergence defined via Jordan decomposition integrals coincides with Araki's relative entropy on arbitrary von Neumann algebras, extending Frenkel's finite-dimensional formula.