Gheondea, A.2016-02-082016-02-0820120378-620Xhttp://hdl.handle.net/11693/21207We 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.English*-representation*-semigroupAdmissible spaceB*-algebraCompletely positive mapDilationHermitian kernelInvariant kernelKolmogorov decompositionpositive semidefinite kernelReproducing kernelVH-spacePrimary 47A20Secondary 43A3546E2246L89Article10.1007/s00020-012-2009-11420-8989