Banach空间中的广义光滑模  

Generalized Modulus of Smoothness in Banach Spaces

作　　者：赵亮[1] 张兴[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2016年第4期112-116,共5页Journal of Harbin University of Science and Technology

基　　金：黑龙江省教育厅科学技术研究项目(12541145)

摘　　要：介于凸性模与广义凸性模具有对偶关系以及广义凸性模有许多优良性质,为了研究是否存在与广义凸性模具有对偶性质的模、若存在这种模那么该模具有什么样的性质等问题.作者从构造与广义凸性模具有对偶性质的模入手,通过应用Hahn-Banach定理找到光滑模的推广形式并给出相应的定义.在给出定义后,作者证明了作为光滑模推广形式的广义光滑模,其能够精确的刻画Banach空间的一致光滑性,并研究了广义光滑模的单调性、奇偶性等性质,最后作为应用给出了Banach空间具有一直正规结构的用广义光滑模刻画的一个充分条件.Since modulus of convexity and generalized convexity mold has dual relationship, and generalized convexity mold has many excellent properties, in order to investigate whether there is a mold has dual nature with generalized modulus of convexity , if there is such a mold, then what properties the mold has. Author constructed the mold which has the dual nature with generalized modulus of convexity to start to find the generalized form smooth mold by applying Hahn-Banach theorem, and the corresponding definitions. After the given definition, the author proves as smooth mold generalized form of generalized modulus of smoothness, it can accurately portray the uniform smoothness of Banach space. Then we study monotonic, parity of modulus of generalized smoothness and other properties. Finally as an application for a Banach space has been a sufficient condition for the uniform formal structure of the generalized modulus of smoothness portrayed.

关 键 词：一致光滑 广义光滑模 Lindenstrauss公式 一致正规结构 

分 类 号：O177.7[理学—数学]