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Equivalence between logarithmic Sobolev inequality and hypercontractivity in a probability gage space

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  17 December 2020

Zhang Lunchuan
Zhang Lunchuan*
Affiliation:
School of Mathematics, Renmin University of China, Beijing100086, P. R. China (zhanglc@ruc.edu.cn)
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Abstract

In this paper, we prove the equivalence between logarithmic Sobolev inequality and hypercontractivity of a class of quantum Markov semigroup and its associated Dirichlet form based on a probability gage space.

Keywords

Quantum Markov semigroupDirichlet formhypercontractivitylogarithmic Sobolev inequality

MSC classification

Primary: 46L53: Noncommutative probability and statistics
Secondary: 46L89: Other “noncommutative” mathematics based on $C^*$-algebra theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 1 , February 2021 , pp. 59 - 71
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Copyright
Copyright © The Author(s) 2020. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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