一类量子Markov半群的超压缩性与对数Sobolev不等式  

Hypercontractivity of a Class of Quantum Markov Semigroups and Logarithmic Sobolev Inequality

作　　者：张伦传[1] Lun Chuan ZHANG(School of Mathematics,Renmin University of China,Beijing 100080,P.R.China)

机构地区：[1]中国人民大学数学学院,北京100080

出　　处：《数学学报（中文版）》2020年第2期149-156,共8页Acta Mathematica Sinica：Chinese Series

摘　　要：本文在有限von Neumann代数生成的非交换概率空间L^p(p≥1)框架下,证明了一类量子Markov半群的超压缩性等价于其对应的Dirichlet型满足对数Sobolev不等式.此结果包含前人的相关成果为特例.作为推论,细化了Biane的相关工作.We prove the equivalence between logarithmic Sobolev inequality and hypercontractivity of quantum Markov semigroup and its associated Dirichlet form based on a probability gage space.Our results include the relevant conclusions of predecessors as special cases,and refine B.Biane’s work as a corollary.

关 键 词：量子Markov半群 超压缩性 DIRICHLET型 对数SOBOLEV不等式 

分 类 号：O177.5[理学—数学]