»ã±¨±êÌâ (Title)£ºNoncommutative logarithmic Sobolev inequalities

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»ã±¨ÈË (Speaker)£º½¹Ó ½ÌÊÚ£¨ÖÐÄÏ´óѧ£©

»ã±¨¹¦·ò (Time)£º2024Äê4ÔÂ10ÈÕ(ÖÜÈý) 10:00

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒ飨514-885-492£©

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»ã±¨ÌáÒª£ºWe show that the logarithmic Sobolev inequality holds for an arbitrary hypercontractive semigroup acting on a noncommutative probability space. Particularly, we can recover the p-logarithmic Sobolev inequality whenever the Riesz transform is bounded. Our inequality applies to numerous concrete cases, including Poisson semigroups for free groups, the Ornstein-Uhlenbeck semigroup for mixed Q-gaussian von Neumann algebras, the free product for Ornstein-Uhlenbeck semigroups etc. This provides a unified abstract approach to logarithmic Sobolev inequalities in noncommutative setting.