Stinespring's Theorem for maps on Hilbert C ∗ -modules

By B. Bhat, G. Ramesh, K. Sumesh. 2010

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Stinespring's representation theorem is a fundamental theorem in the theory of completely positive maps. It is a structure theorem for completely positive maps from a C*- algebra into the C*- algebra of bounded operators on a Hilbert space. This theorem provides a representation for completely positive maps, showing that they are simple modifications of *- homomorphisms. One may consider it as a natural generalization of the well-known Gelfand-Naimark-Segal theorem for states on C*-algebras. Resently, a theorem which looks like Stinesprings theorem was presented by Mohammad B. Asadi in for a class of unital maps on Hilbert C*-modules. This result can also be proved by removing a techical condition of Asadis theorem. The assumption of unitality on maps under consideration can also be remove. This result looks even more like Stinesprings theorem.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

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