von Neumann代数下Markov对偶过程的若干性质  

Some Properties of Markov Dual Branching Process with von Neumann Algebras

作　　者：张一进[1] 李扬荣[2] 

机构地区：[1]重庆邮电大学数理学院,重庆400065 [2]西南大学数学与统计学院,重庆400715

出　　处：《重庆师范大学学报（自然科学版）》2014年第3期58-60,共3页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11201512);重庆邮电大学自然科学基金(No.A2011-19)

摘　　要：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von Neumann代数,M*sa是M的前对偶M*的自伴,T是M*上的Markov积分半群,g∈M*+,η∈R,使得lim sup x→∞ dist(At(T)f,[-g,g])<η,那么M上的正则线性形式的锥体M*+在M*sa中是强规则的。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.

关 键 词：对偶分支Q-矩阵 最小Q函数 对偶 渐近行为 

分 类 号：O177.2[理学—数学]