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Dilations of Some VH-Spaces Operator Valued Invariant Kernels

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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.

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Authors and Affiliations

  1. Department of Mathematics, Bilkent University, 06800, Bilkent, Ankara, Turkey

    Aurelian Gheondea

  2. Institutul de Matematică al Academiei Române, C.P. 1-764, 014700, Bucharest, Romania

    Aurelian Gheondea

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  1. Aurelian Gheondea
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Correspondence to Aurelian Gheondea.

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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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