Modules, completely positive maps, and a generalized KSGNS construction

Details Modules, completely positive maps, and a generalized KSGNS construction Modules, completely positive maps, and a generalized KSGNS construction

2010-07-19

arxiv.org/abs/1007.3218v1

Positivity 15 (3), 509-525 (2011)

Mathematics

Operator Algebras

18 pages

Scientific paper

10.1007/s11117-010-0104-6

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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