On KSGNS representations on Krein \(C^{\ast}\)-modules. (English) Zbl 1310.46048
Summary: Motivated by the notion of the \(P\)-functional, we introduce a notion of \(\alpha\)-completely positive map between \({}^{\ast}\)-algebras which is a Hermitian map satisfying a certain positivity condition, and then a \(\alpha\)-completely positive map which is not completely positive is constructed. We establish the Kasparov-Stinespring-Gelfand-Naimark-Segal constructions of a \(C^{\ast}\)-algebra and \({}^{\ast}\)-algebra on Krein \(C^{\ast}\)-modules with \(\alpha\)-completely positive maps.{
©2010 American Institute of Physics}
©2010 American Institute of Physics}
MSC:
| 46L05 | General theory of \(C^*\)-algebras |
| 46L07 | Operator spaces and completely bounded maps |
| 46L10 | General theory of von Neumann algebras |
| 46L60 | Applications of selfadjoint operator algebras to physics |
| 81R15 | Operator algebra methods applied to problems in quantum theory |
| 81P15 | Quantum measurement theory, state operations, state preparations |
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