广义算子半群的遍历及概率逼近定理  

Ergodic Theory and Probabilistic Approximations for Generalized Operator Semigroups

作　　者：仓定帮[1] 闫守峰[1] 陈藏[2] 魏静[1] 

机构地区：[1]华北科技学院基础部,北京101601 [2]华北科技学院教务处,北京101601

出　　处：《数学年刊（A辑）》2015年第4期389-400,共12页Chinese Annals of Mathematics

基　　金：中央高校基本科研业务基金(No.3142012022;No.3142013039;No.3142014039;No.314201 4017);华北科技学院重点学科建设基金(No.HKXJZD201402)的资助

摘　　要：首先给出了广义算子半群的Abel-遍历和Cesaro-遍历的定义,对两种遍历的性质进行了刻画,研究了两种遍历的等价条件.其次,利用Pettis积分、算子值数学期望及广义连续修正模等工具给出广义算子半群的概率逼近表达式.The definition of Abel-ergodic and Cesaro-ergodic about generalized operator semigroups are given and some characteristics of two ergodicities are discussed. Then the equivalence conditions of two ergodicities are obtained. At last, by means of the Pettis integral, the operator-valued mathematical expect and the generalized continuous modified modulus, the probabilistic approximation and convergent rates are given for generalized operator semigroups.

关 键 词：广义算子半群 遍历 概率逼近 

分 类 号：O177[理学—数学]