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- W4232056575 abstract "We study an extension of the sandwiched Rényi relative entropies for normal positive functionals on a von Neumann algebra, for parameter values $$alpha in [1/2,1)$$ . This work is intended as a continuation of Jenčová (Ann Henri Poincaré 19:2513–2542, 2018), where the values $$alpha >1$$ were studied. We use the Araki–Masuda divergences of Berta et al. (Ann Henri Poincaré 9:1843–1867, 2018) and treat them in the framework of Kosaki’s noncommutative $$L_p$$ -spaces. Using the variational formula, recently obtained by F. Hiai, for $$alpha in [1/2,1)$$ , we prove the data processing inequality with respect to positive trace preserving maps and show that for $$alpha in (1/2,1)$$ , equality characterizes sufficiency (reversibility) for any 2-positive trace preserving map." @default.
- W4232056575 created "2022-05-12" @default.
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- W4232056575 date "2021-06-11" @default.
- W4232056575 modified "2023-10-18" @default.
- W4232056575 title "Rényi Relative Entropies and Noncommutative $$L_p$$-Spaces II" @default.
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- W4232056575 doi "https://doi.org/10.1007/s00023-021-01074-9" @default.
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