Dilations of some VH-spaces operator valued invariant Kernels
Author
Gheondea, A.
Date
2012Source 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
ArticleItem Usage Stats
156
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102
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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/11693/21207Published Version (Please cite this version)
http://dx.doi.org/10.1007/s00020-012-2009-1Collections
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