| 广义算子半群的遍历及概率逼近定理 |
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| 引用本文： | 仓定帮,闫守峰,陈藏,魏静. 广义算子半群的遍历及概率逼近定理[J]. 数学年刊A辑(中文版), 2015, 36(4): 389-400 |
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| 作者姓名： | 仓定帮 闫守峰 陈藏 魏静 |
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| 作者单位： | 华北科技学院基础部, 北京 101601.,华北科技学院基础部, 北京 101601.,华北科技学院教务处, 北京 101601,华北科技学院基础部, 北京 101601. |
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| 基金项目： | 本文受到中央高校基本科研业务基金(No.3142012022, No.3142013039, No.3142014039, & No.314201 4017)和华北科技学院重点学科建设基金(No,HKXJZD201402)的资助. |
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| 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.
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| 关 键 词： | 广义算子半群 遍历 概率逼近 |
Ergodic Theory and Probabilistic Approximations forGeneralized Operator Semigroups |
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| CANG Dingbang,YAN Shoufeng,CHEN Cang and WEI Jing. Ergodic Theory and Probabilistic Approximations forGeneralized Operator Semigroups[J]. Chinese Annals of Mathematics, 2015, 36(4): 389-400 |
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| Authors: | CANG Dingbang YAN Shoufeng CHEN Cang WEI Jing |
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| Abstract: | The definition of Abel-ergodic and Ces`aro-ergodic about generalized operatorsemigroups are given and some characteristics of two ergodicities are discussed. Then theequivalence conditions of two ergodicities are obtained. At last, by means of the Pettisintegral, the operator-valued mathematical expect and the generalized continuous modifiedmodulus, the probabilistic approximation and convergent rates are given for generalizedoperator semigroups. |
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| Keywords: | Generalized operator semigroups Ergodic Probabilistic approximation |
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