paper

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

arXiv:0910.4140

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.

8 pages

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