Gupta, Shefali and G, Ramesh
(2016)
Stinespring's Theorem for Maps on Hilbert C* Modules.
Masters thesis, Indian Institute of Technology Hyderabad.
Abstract
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 wellknown GelfandNaimarkSegal 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.
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