On a connection between Naimark's dilation theorem, spectral representations, and characteristic functions

Mishko Mitkovski

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arXiv · 0910.4140

On a connection between Naimark's dilation theorem, spectral representations, and characteristic functions

Mishko Mitkovski

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Abstract

We give a Herglotz-type representation of an arbitrary generalized spectral measure. As an application, a new proof of the classical Naimark's dilation theorem is given. The same approach is used to describe the spectrum of all unitary rank-one perturbations of a given partial isometry.

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Mishko Mitkovski. 2009-10-21. On a connection between Naimark's dilation theorem, spectral representations, and characteristic functions. https://arxiv.org/abs/0910.4140

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