C-cosine算子函数的遍历性  

Ergodicity for C-cosine Operator Functions

作　　者：肖体俊[1] 梁进[1] 高建伟[2] 

机构地区：[1]中国科学技术大学数学系,安徽合肥230026 [2]河北工业大学数学系,天津300130

出　　处：《应用泛函分析学报》1999年第2期97-107,共11页Acta Analysis Functionalis Applicata

摘　　要：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.

关 键 词：C-cosine算子函数 Abel遍历 Cesàro遍历 轨道遍历 K-泛函 非最优化速率 

分 类 号：O177[理学—数学]