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 $C^{\ast }$-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.

18 pages

References in corpus (2)

• Positive sesquilinear form measures and generalized eigenvalue expansions
• Diagonalization and representation results for nonpositive sesquilinear form measures

Cited by in corpus (3)

• Completely positive maps on modules, instruments, extremality problems, and applications to physics
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• Barycentric decomposition for quantum instruments