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About: Sz.-Nagy's dilation theorem     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatTheoremsInFunctionalAnalysisyago:Abstraction100002137yago:Communication100033020yago:Message106598915yago:Proposition106750804yago:Statement106722453yago:Theorem106752293 New Facet based on Instances of this Class

The Sz.-Nagy dilation theorem (proved by Béla Szőkefalvi-Nagy) states that every contraction T on a Hilbert space H has a unitary dilation U to a Hilbert space K, containing H, with Moreover, such a dilation is unique (up to unitary equivalence) when one assumes K is minimal, in the sense that the linear span of ∪nUnH is dense in K. When this minimality condition holds, U is called the minimal unitary dilation of T.