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SUMMARY:Ivan Bardet (Univ. Lyon)
DTSTART:20210609T130000Z
DTEND:20210609T134500Z
DTSTAMP:20260423T004516Z
UID:Opalg21/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Opalg21/6/">
 Approximate tensorization of the relative entropy for noncommuting conditi
 onal expectations</a>\nby Ivan Bardet (Univ. Lyon) as part of Conference o
 n operator algebras and related topics in Istanbul\, 2021\n\n\nAbstract\nI
  will present a new generalisation of the strong subadditivity of the entr
 opy to the setting of general conditional expectations onto arbitrary fini
 te-dimensional von Neumann algebras. The latter inequality\, which we call
  approximate tensorization of the relative entropy\, can be expressed as a
  lower bound for the sum of relative entropies between a given density and
  its respective projections onto two intersecting von Neumann algebras in 
 terms of the relative entropy between the same density and its projection 
 onto an algebra in the intersection\, up to multiplicative and additive co
 nstants. In particular\, our inequality reduces to the so-called quasi-fac
 torization of the entropy for commuting algebras\, which is a key step in 
 modern proofs of the logarithmic Sobolev inequality for classical lattice 
 spin systems.\n
LOCATION:https://researchseminars.org/talk/Opalg21/6/
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