On KSGNS representations on Krein C*-modules

초록

Motivated by the notion of P-functional, we introduce a notion of alpha-completely positive map between *-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 C*-algebra and *-algebra on Krein C*-modules with alpha-completely positive maps.

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