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Unitary point spectrum of almost unitary operators. (Russian. English summary) Zbl 0533.47050

Let L be an almost unitary operator acting in the separable Hilbert space H (i.e. L is the sum of unitary and Kernel operators). Let \(\sigma_ p(L)\) be the point spectrum of the operator L, and E be a subset of the unit circle T. \(C_{\sigma}\) denotes the union of all sets of T, which are represented by a countable union of Carleson sets. The author proves that the set E is the unitary point spectrum of a certain almost unitary operator, if and only if \(E\in C_{\sigma}\). This result is connected with the following result.
In order that there exists a function \(h\in H^ 2\) such that \(h\neq 0\) and \(E=\{\lambda \in T:\quad \frac{h}{z-\lambda}\in H^ 2\}\) it is necessary and sufficient that \(E\in(C_{\sigma})\).
Reviewer: M.Shahin

MSC:

47A12 Numerical range, numerical radius
47A10 Spectrum, resolvent
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