| 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,2018,39(2):199~210 |
| 一类 Markov 模算子半群与相应的算子值 Dirichlet 型刻画 |
| Characterization of Class of Markov Module Operator Semigroups and the Corresponding Operator-Valued Dirichlet Forms |
| Received:October 16, 2015 Revised:January 06, 2017 |
| DOI：10.16205/j.cnki.cama.2018.0019 |
| 中文关键词: ${rm II}_1$型因子, Hilbert $w^*${-}双模, Markov 模算子半群, 算子值 Dirichlet 型 |
| 英文关键词:${rm II}_1$ factor, Hilbert $w^*$-bimodule, Markov module operator semigroup, Operator-valued Dirichlet form |
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| 中文摘要: |
| 本文基于${\rm II}_1${-}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. |
| 英文摘要: |
| 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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