Naimark's dilation theorem

In operator theory, Naimark's dilation theorem is a result that characterizes positive operator valued measures. It can be viewed as a consequence of Stinespring's dilation theorem.

In the mathematical literature, one may also find other results that bear Naimark's name.

In the physics literature, it is common to see the spelling “Neumark” instead of “Naimark.” The latter variant is according to the romanization of Russian used in translation of Soviet journals, with diacritics omitted (originally Naĭmark). The former is according to the etymology of the surname.

Let X be a compact Hausdorff space, H be a Hilbert space, and L(H) the Banach space of bounded operators on H. A mapping E from the Borel σ-algebra on X to ${\displaystyle L(H)}$ is called a operator-valued measure if it is weakly countably additive, that is, for any disjoint sequence of Borel sets ${\displaystyle \{B_{i}\}}$, we have

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