Some Properties of Markov Dual Branching Process with von Neumann Algebras
Zhang Yi-ji · Chongqing Shifan Daxue xuebao. Ziran kexue ban · 2014
In this paper,with introduction of the theory of operator semigroup,some properties of Q-Matrix and minimal Q-function 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;Mis von Neumann algebra,M*sais predual M*of M,Tis a Markov integrated semigroup on M*,g∈M*+,η∈R,such that lim sup x→∞ dist(At(T)f,[-g,g])η,then the cone M*+of positive normal linear forms on Mis strongly normal in M*sa