# Quasi-entropies for States of a von Neumann Algebra

@article{Petz1985QuasientropiesFS, title={Quasi-entropies for States of a von Neumann Algebra}, author={D{\'e}nes Petz}, journal={Publications of The Research Institute for Mathematical Sciences}, year={1985}, volume={21}, pages={787-800} }

In a general von Neumann algebra context the relative entropy of two states was defined and investigated by Araki ([3], see also [5]). When <p and w are normal states on a von Neuman algebra M the relative entropy S(<p,<u) is defined by means of the relative modular operator A (cp, co). r-<logJ(p,a00,0> if J(0>)>j(o0. S(<p 9 co) = \. v + oo otherwise. where Q is the representing vector for co in the natural positive cone of the standard form of M and $(•) denotes the support of a functional. We…

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