C-cosine算子函数的遍历性

Ergodicity for C-cosine Operator Functions

在本文中，我们定义了 Ｃ－ｃｏｓｉｎｅ算子函数的 Ａｂｅｌ遍历性与Ｃｅｓàｒｏ遍历性，讨论了Ｃ－ｃｏｓｉｎｅ算子函数这两种遍历性的相互关系及基本性质，得到了其强Ａｂｅｌ遍历性在Ｒ（Ｃ）稠时的完全刻划．此外，我们还讨论了Ｃ－ｃｏｓｉｎｅ算子函数的轨道遍历性，并借助于Ｋ－泛函，给出了Ｃ－ｃｏｓｉｎｅ算子函数在０点以非最优化速率收敛的一个充要条件．

In this paper, the Abel-ergodicity and Cesàro-ergodicity for C-cosine operator functions on Banach spaces X are defined. The relationship between the two kinds of ergodic properties is investigated. Some related basic properties are shown. A characterization of Abel-ergodicity is established in the case of R(C) being dense in X. Moreover, the orbit-ergodicity for C-cosine operator functions is defined and dis- cussed. A sufficient and necessary condition is given in terms of K-functional, ensuring the convergence at non-optimal rates of C-cosine operator functions at 0.