| 一类 Markov 模算子半群与相应的算子值 Dirichlet 型刻画 |
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| 引用本文： | 张伦传.一类 Markov 模算子半群与相应的算子值 Dirichlet 型刻画[J].数学年刊A辑(中文版),2018,39(2):199-210. |
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| 作者姓名： | 张伦传 |
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| 作者单位： | 中国人民大学信息学院数学系 |
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| 摘 要： | 本文基于Ⅱ_1-型因子把非交换对称Dirichlet型理论推广到算子值情形.在此框架下建立了算子值Dirichlet型,Markov模算子半群及Markov预解集之间的一一对应关系.
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| 关 键 词： | ${rm II}_1$型因子 Hilbert $w^*${-}双模 Markov 模算子半群 算子值 Dirichlet 型 |
| 收稿时间： | 2015/10/16 0:00:00 |
| 修稿时间： | 2017/1/6 0:00:00 |
Characterization of Class of Markov Module Operator Semigroups and the Corresponding Operator-Valued Dirichlet Forms |
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| ZHANG Lunchuan.Characterization of Class of Markov Module Operator Semigroups and the Corresponding Operator-Valued Dirichlet Forms[J].Chinese Annals of Mathematics,2018,39(2):199-210. |
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| Authors: | ZHANG Lunchuan |
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| Institution: | Department of Mathematics, Renmin University of China, Beijing 100086, China. |
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| Abstract: | The theory of noncommutative symmetric Dirichlet forms is generalized to the operator-valued cases
based on ${\rm II}_1$ factor. The author
establishes the natural correspondence among operator-valued Dirichlet forms,
Markov module operator semigroups and Markovian resolvents within this context. |
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| Keywords: | ${rm II}_1$ factor Hilbert $w^*$-bimodule Markov module operator semigroup Operator-valued Dirichlet form |
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