Banach空间中极限集与极限算子的弱化  

The weakness of limited set and limited operator in Banach spaces

作　　者：林鸿钊[1] 

机构地区：[1]福建农林大学计算机与信息学院应用数学系,福建福州350002

出　　处：《纯粹数学与应用数学》2011年第5期650-655,共6页Pure and Applied Mathematics

基　　金：2009年福建省教育厅A类科技项目(JA09072)

摘　　要：为了进一步研究Banach空间中集合的紧致性,受极限集与极限算子定义的启发,给出了弱极限集与弱极限算子的定义,得到了它们的等价刻画,利用空间结构与算子理想的互动关系证明了弱极限算子全体是Pietsch意义下的闭满射算子理想.For the further study of the set compactness on Banach spaces, we give the definition of weak limited set and weak limited operator in light of the definition of limited set and the limited operator, and obtain their equivalent characterization respectively. By means of the interaction between Banach spaces structure and operator ideals, it was proved that all weak limited operators between Banach spaces constitute a closed surjective general operator ideal in the sense of Pietsch.

关 键 词：弱极限集 弱极限算子 算子理想 

分 类 号：O177[理学—数学]