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Modules, completely positive maps, and a generalized KSGNS construction

Published 19 Jul 2010 in math.OA and math.FA | (1007.3218v1)

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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