Modules, completely positive maps, and a generalized KSGNS construction
Abstract: A very general KSGNS type dilation theorem in the context of right (not necessarily Hilbert) modules over $C*$-algebras is presented. The proof uses Kolmogorov type decompositions for positive-definite kernels with values in spaces of sesquilinear maps. More specific functional analytic applications are obtained by adding assumptions.
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