Dilations of some VH-spaces operator valued invariant Kernels

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2012

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Gheondea, A.

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Abstract

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.

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Integral Equations and Operator Theory

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Springer

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Published Version (Please cite this version)

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English