High Quality Content by WIKIPEDIA articles! The Sz.-Nagy dilation theorem (proved by Bela Sz?kefalvi-Nagy) states that every contraction T on a Hilbert space H has a unitary dilation U to a Hilbert space K. Moreover, such a dilation is unique (up to unitary equivalence) when one assumes K is minimal, in the sense that the linear span of ?nUnK is dense in K. When this minimality condition holds, U is called the minimal unitary dilation of T. The Schaffer form of a unitary Sz. Nagy dilation can be viewed as a beginning point for the characterization of all unitary dilations, with the required property, for a given contraction. To see that this generalises Sz.-Nagy's theorem, note that contraction operators have the unit disc D as a spectral set, and that normal operators with spectrum in the unit circle ?D are unitary.

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