On a connection between Naimark's dilation theorem, spectral representations, and characteristic functions
Mishko Mitkovski
47A2047A4530J99Naimark's dilation theoremgeneralized spectral measurecharacteristic functionrank-one perturbations of a partial isometry
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.
Indiana University Mathematics Journal
2011
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10.1512/iumj.2011.60.4175
10.1512/iumj.2011.60.4175
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Indiana Univ. Math. J. 60 (2011) 507 - 516
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