p-算子空间上的框架逼近和嵌入  

Frame Approximation and Embedding for p-operator Spaces

作　　者：安桂梅[1] 李磊[1] 刘锐[1] 

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

出　　处：《数学学报（中文版）》2017年第1期123-132,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11671214;11301285;11201336;11101220)

摘　　要：介绍了p-算子空间上的p-完全有界框架概念.证明了可分p-算子空间X上存在p-完全有界框架当且仅当X满足p-完全有界逼近性质当且仅当X能够p-完全可补嵌入有p-完全有界基的p-算子空间.对于满足p-完全有界逼近性质的非可分的p-算子空间,还证明了其任意可分子空间均可以p-完全同构嵌入到有p-完全有界框架的p-算子空间.We introduce the concept of p-completely bounded frames for p-operator spaces. We prove that a separable p-operator space X has a p-completely bounded frame if and only if it has the p-completely bounded approximation property if and only if it can be p-completely complementedly embedded into a p-operator space with a p- completely bounded basis. For a non-separable p-operator space with the p-completely bounded approximation property, we prove that its separable subspace always can be p-completely isomorphically embedded into a p-operator space with a p-completely bounded frame.

关 键 词：p-算子空间 p-完全有界框架 p-完全有界逼近性质 p-完全有界基 

分 类 号：O177[理学—数学]