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Quantum $f$-divergences in von Neumann algebras I. Standard $f$-divergences

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 نشر من قبل Fumio Hiai
 تاريخ النشر 2018
  مجال البحث فيزياء
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 تأليف Fumio Hiai




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We make a systematic study of standard $f$-divergences in general von Neumann algebras. An important ingredient of our study is to extend Kosakis variational expression of the relative entropy to an arbitary standard $f$-divergence, from which most of the important properties of standard $f$-divergences follow immediately. In a similar manner we give a comprehensive exposition on the Renyi divergence in von Neumann algebra. Some results on relative hamiltonians formerly studied by Araki and Donald are improved as a by-product.



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