Banach空间的β算子  

β-operator in Banach Spaces

作　　者：樊丽颖[1] 张佳宁 曹丽萍 宋婧婧 FAN Li-ying;ZHANG Jia-ning;CAO Li-ping;SONG Jing-jing(Department of Applied Mathematics,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学应用数学系,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2018年第2期140-143,共4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(12541161)

摘　　要：为了研究Banach空间算子的一些几何性质,给出了β算子和弱β算子的定义;讨论了β算子和弱β算子的性质,进一步得到了算子具有β性质的充分必要条件、β算子与具有β性质的空间之间的关系,研究了β算子空间的定义及此空间的性质,得到了β算子是紧算子的判别条件,给出了自反空间一个新的特征。To study some geometric properties of Banach space operator,the definitions of theβ-operator and weakβ-operator were given,and the properties of theβ-operator and weakβ-operator were discussed.Sufficient and necessary conditions for the operator withβ-property were obtained.The relationship between properties ofβ-operator and the space which hasβ-property were discussed.The definition ofβ-operator space and the property of this space were studied.The conclusion was obtained thatβ-operator is a compact operator,and a new feature of reflexive space was given.

关 键 词：β算子 自反空间 弱β算子 β算子空间 

分 类 号：O177.7[理学—数学]