Dilations of some VH-spaces operator valued invariant Kernels
Integral Equations and Operator Theory
451 - 479
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We investigate VH-spaces (Vector Hilbert spaces, or Loynes spaces) operator valued Hermitian kernels that are invariant under actions of *-semigroups from the point of view of generation of *-representations, linearizations (Kolmogorov decompositions), and reproducing kernel spaces. We obtain a general dilation theorem in both Kolmogorov and reproducing kernel space representations, that unifies many dilation results, in particular B. Sz.-Nagy's and Stinesprings' dilation type theorems. © 2012 Springer Basel.
Completely positive map
positive semidefinite kernel
Published Version (Please cite this version)http://dx.doi.org/10.1007/s00020-012-2009-1
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