×

Frame approximation and embedding for \(p\)-operator spaces. (Chinese. English summary) Zbl 1389.47185

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)
PDFBibTeX XMLCite