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arXiv · 1007.3218

Modules, completely positive maps, and a generalized KSGNS construction

Juha-Pekka Pellonpää·Kari Ylinen
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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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Juha-Pekka Pellonpää, Kari Ylinen. 2010-07-19. Modules, completely positive maps, and a generalized KSGNS construction. https://doi.org/10.1007/s11117-010-0104-6

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