| 一类量子Markov半群的超压缩性与对数Sobolev不等式 |
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| 引用本文： | 张伦传. 一类量子Markov半群的超压缩性与对数Sobolev不等式[J]. 数学学报, 2020, 63(2): 149-156 |
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| 作者姓名： | 张伦传 |
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| 作者单位： | 中国人民大学数学学院 北京 100080 |
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| 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.
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| 关 键 词： | 量子Markov半群 超压缩性 DIRICHLET型 对数SOBOLEV不等式 |
Hypercontractivity of a Class of Quantum Markov Semigroups and Logarithmic Sobolev Inequality |
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| Lun Chuan ZHANG. Hypercontractivity of a Class of Quantum Markov Semigroups and Logarithmic Sobolev Inequality[J]. Acta Mathematica Sinica, 2020, 63(2): 149-156 |
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| Authors: | Lun Chuan ZHANG |
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| Affiliation: | School of Mathematics, Renmin University of China, Beijing 100080, P. R. China |
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| Abstract: | 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. |
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| Keywords: | Quantum Markov semigroup hypercontractivity Dirichlet form logarithmic Sobolev inequality |
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