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      Dilations of some VH-spaces operator valued invariant Kernels

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      Author
      Gheondea, A.
      Date
      2012
      Source Title
      Integral Equations and Operator Theory
      Print ISSN
      0378-620X
      Electronic ISSN
      1420-8989
      Publisher
      Springer
      Volume
      74
      Issue
      4
      Pages
      451 - 479
      Language
      English
      Type
      Article
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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.
      Keywords
      *-representation
      *-semigroup
      Admissible space
      B*-algebra
      Completely positive map
      Dilation
      Hermitian kernel
      Invariant kernel
      Kolmogorov decomposition
      positive semidefinite kernel
      Reproducing kernel
      VH-space
      Primary 47A20
      Secondary 43A35
      46E22
      46L89
      Permalink
      http://hdl.handle.net/11693/21207
      Published Version (Please cite this version)
      http://dx.doi.org/10.1007/s00020-012-2009-1
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      • Department of Mathematics 628
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