An, Guimei; Li, Lei; Liu, Rui Frame approximation and embedding for \(p\)-operator spaces. (Chinese. English summary) Zbl 1389.47185 Acta Math. Sin., Chin. Ser. 60, No. 1, 123-132 (2017). Summary: 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. MSC: 47L25 Operator spaces (= matricially normed spaces) Keywords:\(p\)-operator space; \(p\)-completely bounded frame; bounded approximation property; bounded basis PDFBibTeX XMLCite \textit{G. An} et al., Acta Math. Sin., Chin. Ser. 60, No. 1, 123--132 (2017; Zbl 1389.47185)