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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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