Ryszard Pawel Kostecki

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We use the Falcone–Takesaki non-commutative flow of weights and the resulting theory of non-commutative Lp spaces in order to define the family of relative entropy functionals that naturally generalise the quantum relative entropies of Jenčová– Ojima and the classical relative entropies of Zhu–Rohwer, and belong to an intersection of families of Petz(More)
We introduce, and investigate the properties of, the family of quantum Brègman distances, based on embeddings into suitable vector spaces (with the reflexive noncommutative Orlicz spaces over semi-finite W-algebras and noncommutative Lp spaces over any W-algebras providing two important examples). This allows us to define geometric categories for nonlinear(More)
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