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The generalized Wold decomposition for subnormal operators. (English) Zbl 0645.47021
Let S be a subnormal operator on a Hilbert space and N its minimal normal extension. If $$\Omega$$ is a finitely connected domain bounded by Jordan curves such that the spectrum of S is contained in $$\Omega$$ and the spectrum of N is contained in $$\partial \Omega$$, M. B. Abrahamse and R. G. Douglas [Adv. Math. 19, 106-148 (1976; Zbl 0321.47019)] have shown that S can be represented as the direct sum of a normal operator and a bundle shift over $$\Omega$$ (i.e. an operator $$f\mapsto zf$$ for $$f\in H^ 2[E]$$ where E is a certain flat unitary bundle over $$\Omega$$ and $$H^ 2[E]$$ consists of those analytic sections $$\phi$$ of E for which the functions $$z\mapsto \| \phi (z)\|^ 2$$ have harmonic majorants on $$\Omega)$$. In the present paper this Wold decomposition is extended to the case of subnormal operators with less restrictive conditions on $$\Omega$$. For the proof a result about the absolute continuity of the spectral measure of N with respect to the harmonic measure on $$\partial \Omega$$ and a Beurling-type description of invariant subspaces are obtained.
Reviewer: G.Garske

##### MSC:
 47B20 Subnormal operators, hyponormal operators, etc. 47A10 Spectrum, resolvent 47A15 Invariant subspaces of linear operators
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##### References:
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