双连续余弦函数的Cesàro遍历定理

Cesàro ergodic theorems for bi-continuous cosine functions

Banach空间算子半群的应用研究中,范数意义下强连续这样的要求较强,在实际中发现存在一些半群并不是强连续的。基于双连续半群的概念,给出双连续余弦函数的概念及性质,进而对双连续余弦函数的Cesàro遍历的定义及性质进行研究,得到在拓扑意义下的双连续余弦函数的Cesàro遍历的若干结果。

For many applications of operator semigroups on Banach spaces, strong continuity with respect to the norm is a too strong requirement. In fact, there exists a class of semigroups of operators which the usual strong continuity fails to hold. Based on the concept of bi-continuous operators, the con- cept and main properties of bi-continuous cosine function were introduced, and then the description of the main properties and the convergence of Cesaro ergodicity for bi-continuous cosine functions were studied. More precisely, some results on the Cesiaro ergodicity the topology τ are proved. for bi-continuous cosine functions with respect to