article

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

Authors: Mishko Mitkovski

Issue: Volume 60 (2011), Issue 2, 507-516

Abstract:

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