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

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

2009-10-21

arxiv.org/abs/0910.4140v1

Mathematics

Functional Analysis

8 pages

Scientific paper

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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