双连续C余弦函数的遍历定理  

Ergodic theorems for bi-continuous C Cosine Functions

作　　者：仓定帮[1] 刘瑞芹[1] 陈藏[1] 

机构地区：[1]华北科技学院

出　　处：《暨南大学学报（自然科学与医学版）》2014年第2期210-214,共5页Journal of Jinan University(Natural Science & Medicine Edition)

基　　金：国家自然科学基金资助(10671205);中央高校基本科研资助基金(3142014039;3142013039;3142014127);华北科技学院重点学科建设基金资助(HKXJZD201402)

摘　　要：实际研究中发现有些问题所对应的半群并不是强连续的,可以在Banach空间上赋予一个比范数拓扑粗的局部凸拓扑",使得半群在"下强连续.基于此在给出了Banach空间上双连续双连续C余弦函数的概念及其性质的基础上,重点讨论了双连续C余弦函数的遍历的定义及性质,得到了在拓扑"意义下的双连续C余弦函数的遍历的若干结果.For many applications of operator semigroups,strong continuity with respect to the norm of a Banach space is a too strong requirement.In fact,there exist a class of semigroups of operators which the usual strong continuity fails to hold.Based on the concept of bi-continuous operators,the concept and main properties of bi-continuous cosine function were introduced and then the description of the main properties and the convergence for bi-continuous C cosine functions were given.More precisely,some re-sults on the mean ergodicity for bi-continuous C cosine functions with respect to the topology t are proved.

关 键 词：双连续C余弦函数 遍历性 局部凸拓扑 

分 类 号：O177.2[理学—数学]