The unitary part of class $${\mathcal F}$$-contractions.(English)Zbl 0939.47017

Let $$H$$ be a Hilbert space and let $$F$$ denote the class of bounded linear operators on $$H$$ with Fuglede’s property. It is proved that if $$T$$ from $$F$$ is a contraction then the positive square root of the strong limit of $$T^nT^{*n}$$ is a projection operator from $$H$$ onto the maximal reducing subspace of $$T$$ where its restriction is unitary.

MSC:

 47B20 Subnormal operators, hyponormal operators, etc. 47A65 Structure theory of linear operators
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References:

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