von Neumann代数下Markov对偶过程的若干性质

本文引入Markov算子半群的理论，利用分析和代数的方法研究了Markov对偶过程的Q矩阵和最小Q函数的若干性质。主要结论有：对偶分支Q-矩阵是忠实的、次随机单调的及正则的、零流出的、对偶的；对偶分支矩阵的最小Q函数F（t）是唯一且忠实的，非随机单调的及对偶的；M是vonNeumann代数，M＊sa是M的前对偶M＋的自伴，T是Mn上的Markov积分半群，g∈M，＋，η∈R，使得limsupdist（At（T）f，-g，g]）〈η，那么M上的正则线性形式的锥体Mn＋在M＊sa中是强规则的。

Some Properties of Markov Dual Branching Process with von Neumann Algebras

In this paper, with introduction of the theory of operator semigroup, some properties of Q-Matrix and minimal Q-func- tion of Markov dual branching process are studied by the method of analysis and algebras. Some important results are obtained, such as Dual Branching Q-Matrix is honest, substochastic monotone, regular, zero-exit and dual; minimal Q-function of Markov dual branching matrix is unique and honest, not stochastic monotone, dual; M is von Neumann algebra, Mn is predual M. of M, T is a Markov integrated semigroup on M. , g ∈ M. ＋ , η∈ R, such that lim sup dist（A, （T）f, -g, g3）〈η, then the cone M. ＋ of positive normal linear forms on M is strongly normal in M＊sa.