中文摘要：

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．

英文摘要：

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.