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Positive maps over \(\sigma\)-\(C^*\)-algebras. (Chinese. English summary) Zbl 0984.46036

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.

MSC:

46L05 General theory of \(C^*\)-algebras
46L99 Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.)
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