Dilations of Some VH-Spaces Operator Valued Invariant Kernels
Please cite this item using this persistent URL
http://hdl.handle.net/11693/21207Journal
Integral Equations and Operator Theory
Published as
http://dx.doi.org/10.1007/s00020-012-2009-1Collections
- Research Paper [6026]
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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