Banach空间与格上的逼近性质和算子扩张理论  

Approximation property and operator dilation theory of Banach spaces and lattices

作　　者：包琪瑶 胡前锋 蒋兴妮 刘锐[1] Qiyao Bao;Qianfeng Hu;Xingni Jiang;Rui Liu

机构地区：[1]南开大学数学科学学院,天津300071 [2]河北工业大学理学院,天津300401 [3]四川大学数学学院,四川610065

出　　处：《中国科学：数学》2023年第12期1545-1560,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12071230,11971348和12201439);南开大学百名青年学科带头人计划(批准号:ZB22000105,63223027,91923104,91823003和63174012)资助项目。

摘　　要：本文介绍近期发展的Banach空间扩张理论的主要结果,在此基础上利用Banach空间有界逼近性质与Schauder框架的等价关系,研究了有有界逼近性质的Banach空间上算子值测度的扩张和有限秩算子的扩张,并得到算子空间上完全有界算子值测度的扩张结果.最后,考虑具有Schauder框架的Banach格上的算子值测度的扩张,主要关注其基本扩张空间的偏序结构,以及扩张中各映射对偏序结构的保持性质.In this paper,we introduce the main results of Banach space dilation theory.Based on this,and using the equivalent relation between the bounded approximation property of Banach spaces and Schauder frames,we study the dilation of operator-valued measures and finite rank operators on Banach spaces with the bounded approximation property.We also obtain the dilation result of the completely bounded operator-valued measures on operator spaces.Finally,we also consider the dilation of operator-valued measures on Banach lattices with Schauder frames.We mainly focus on the partial order structure of the elementary dilation spaces and the preserved properties of the maps in the dilation to the partial order structure.

关 键 词：扩张理论 算子值测度 有界逼近性质 算子空间 BANACH格 

分 类 号：O177.2[理学—数学]