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

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.
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.