Dilations of Some VH-Spaces Operator Valued Invariant Kernels
نویسنده
چکیده
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. Mathematics Subject Classification (2010). Primary 47A20; Secondary 43A35, 46E22, 46L89.
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