Makarov, N. G. Unitary point spectrum of almost unitary operators. (Russian. English summary) Zbl 0533.47050 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 126, 143-149 (1983). 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 Cited in 1 Review MSC: 47A12 Numerical range, numerical radius 47A10 Spectrum, resolvent Keywords:almost unitary operator; Kernel operators; point spectrum; Carleson sets; unitary point spectrum PDFBibTeX XMLCite \textit{N. G. Makarov}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 126, 143--149 (1983; Zbl 0533.47050) Full Text: EuDML