scholarly journals Ergodic properties of Markov semigroups in von Neumann algebras

2020 ◽  
Vol 64 ◽  
pp. 283-331
Author(s):  
Katarzyna Kielanowicz ◽  
Andrzej Łuczak
Keyword(s):  
Von Neumann Algebras ◽  
Markov Semigroups ◽  
Von Neumann ◽  
Ergodic Properties

scholarly journals Complete Gradient Estimates of Quantum Markov Semigroups

2021 ◽  
Vol 387 (2) ◽  
pp. 761-791
Author(s):  
Melchior Wirth ◽  
Haonan Zhang
Keyword(s):  
Von Neumann Algebras ◽  
Logarithmic Sobolev Inequality ◽  
Wasserstein Distance ◽  
Gradient Estimate ◽  
Gradient Estimates ◽  
Markov Semigroups ◽  
Free Products ◽  
Von Neumann ◽  
Symmetric Quantum ◽  
Poisson Type

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.

scholarly journals Relative entropy for von Neumann subalgebras

2020 ◽  
Vol 31 (06) ◽  
pp. 2050046
Author(s):  
Li Gao ◽  
Marius Junge ◽  
Nicholas LaRacuente
Keyword(s):  
Relative Entropy ◽  
Von Neumann Algebras ◽  
Markov Semigroups ◽  
Von Neumann ◽  
Decoherence Time ◽  
Rényi Relative Entropy ◽  
Finite Von Neumann Algebras

We revisit the connection between index and relative entropy for an inclusion of finite von Neumann algebras. We observe that the Pimsner–Popa index connects to sandwiched [Formula: see text]-Rényi relative entropy for all [Formula: see text], including Umegaki’s relative entropy at [Formula: see text]. Based on that, we introduce a new notation of relative entropy to a subalgebra which generalizes subfactors index. This relative entropy has application in estimating decoherence time of quantum Markov semigroups.

On ergodic properties of operator nets on the predual of von neumann algebras

2018 ◽  
Vol 55 (4) ◽  
pp. 479-486
Author(s):  
Nazife Erkurşun Özcan
Keyword(s):  
Asymptotic Stability ◽  
Lower Bound ◽  
Von Neumann Algebras ◽  
Von Neumann ◽  
Ergodic Properties ◽  
Special Operator ◽  
Operator Nets

In this paper, we proved theorems which give the conditions that special operator nets on a predual of von Neumann algebras are strongly convergent under the Markov case. Moreover, we investigate asymptotic stability and existence of a lower-bound function for such nets.

Sign in / Sign up

Export Citation Format

Share Document