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.
作者
张伦传
Lun Chuan ZHANG(School of Mathematics,Renmin University of China,Beijing 100080,P.R.China)
出处
《数学学报（中文版）》
CSCD
北大核心
2020年第2期149-156,共8页
Acta Mathematica Sinica：Chinese Series
