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.
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This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS UEFISCDI, project number PN-II-ID-PCE-2011-3-0119.
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Gheondea, A. Dilations of Some VH-Spaces Operator Valued Invariant Kernels. Integr. Equ. Oper. Theory 74, 451–479 (2012). https://doi.org/10.1007/s00020-012-2009-1
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DOI: https://doi.org/10.1007/s00020-012-2009-1