Complete Gradient Estimates of Quantum Markov Semigroups
2021 ◽
Vol 387
(2)
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pp. 761-791
Keyword(s):
AbstractIn this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors.
1973 ◽
Vol 178
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pp. 147-147
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2015 ◽
Vol 26
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pp. 1550003
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2006 ◽
Vol 314
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pp. 749-763
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Vol 05
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pp. 571-579
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2010 ◽
Vol 43
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pp. 63-74
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