Xu, Tianzhou Positive maps over \(\sigma\)-\(C^*\)-algebras. (Chinese. English summary) Zbl 0984.46036 J. Syst. Sci. Math. Sci. 21, No. 1, 1-8 (2001). Summary: We develop the part of the theory of \(\sigma\)-\(C^*\)-algebras. In particular, we discuss positive linear functionals, completely positive maps, and \(n\)-positive linear functionals over \(\sigma\)-\(C^*\)-algebras to this setting, including a criterion positivity and the classical GNS-representation. Cited in 1 Document MSC: 46L05 General theory of \(C^*\)-algebras 46L99 Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.) Keywords:\(\sigma\)-\(C^*\)-algebras; positive linear functionals; completely positive maps; \(n\)-positive linear functionals; GNS-representation PDFBibTeX XMLCite \textit{T. Xu}, J. Syst. Sci. Math. Sci. 21, No. 1, 1--8 (2001; Zbl 0984.46036)