| p-算子空间上的框架逼近和嵌入 |
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| 引用本文： | 安桂梅,李磊,刘锐. p-算子空间上的框架逼近和嵌入[J]. 数学学报, 2017, 60(1): 123-132 |
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| 作者姓名： | 安桂梅 李磊 刘锐 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金资助项目（11671214，11301285，11201336，11101220） |
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| 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.
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| 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 |
Frame Approximation and Embedding for p-operator Spaces |
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| Gui Mei AN,Lei LI,Rui LIU. Frame Approximation and Embedding for p-operator Spaces[J]. Acta Mathematica Sinica, 2017, 60(1): 123-132 |
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| Authors: | Gui Mei AN Lei LI Rui LIU |
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| Affiliation: | School of Mathematical Science and LPMC, Nankai University, Tianjin 300071, P. R. China |
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| Abstract: | 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 pcompletely 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. |
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| Keywords: | p-operator space p-completely bounded frame p-completely bounded approximation property p-completely bounded basis |
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