双连续C余弦函数的遍历定理

摘要

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 !are proved.%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。