Modules, completely positive maps, and a generalized KSGNS construction

: Pellonpaa JP, Ylinen K

Publisher: SPRINGER

: 2011

: Positivity

: POSITIVITY

: 3

: 15

: 3

: 509

: 525

: 17

: 1385-1292

DOI: https://doi.org/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.