Banach与算子空间上的逼近性质和框架（英文）  

Approximation properties and frames for Banach and operator spaces

作　　者：胡前锋 刘锐[2] HU Qianfeng;LIU Rui(School of Mathematical Sciences,Nankai University,Tianjin 300071,China;The Key Laboratory of Pure Mathematics and Combinatorics,Ministry of Education,Tianjin 300071,China)

机构地区：[1]南开大学数学科学学院,天津300071 [2]核心数学与组合数学教育部重点实验室,天津300071

出　　处：《苏州科技大学学报（自然科学版）》2019年第3期1-6,19,共7页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11671214);南开大学百名青年领军人才项目(91923104;91823003;63174012);中央高校基本科研业务费专项基金资助项目(63191503;63171225)

摘　　要：论文给出关于Banach与算子空间上的逼近性质和框架的近期工作中主要成果的综述。通过介绍Schauder框架和完全有界框架,给出Banach空间的逼近性质与算子空间的完全有界逼近性质的等价刻画。同时也给出一些具体例子以及关于可补嵌入的对偶理论,并介绍了一些公开问题。We have made a survey of the main results on approximation properties and frames for Banach spaces and operator spaces.By introducing Schauder frame and completely bounded frame,we have presented the equivalent characterizations of the bounded approximation properties for Banach spaces and the completely bounded approximation properties for operator spaces.We have also provided some examples and the duality theory on complemented embedding,and introduced some open questions.

关 键 词：逼近性质 BANACH空间 全有界框架 算子空间 SCHAUDER基 

分 类 号：O177.2[理学—数学]