Lee, Woo Young Cowen sets for Toeplitz operators with finite rank selfcommutators. (English) Zbl 1100.47025 J. Oper. Theory 54, No. 2, 261-267 (2005). The Cowen set for the function \(\varphi\in L^{\infty}(\mathbb{T})\) is defined as \[ \mathcal{E}(\varphi)= \{k\in H^{\infty}(\mathbb{T}):\| k\| _{\infty}\leq 1\;\text{and}\;\varphi-k\bar{\varphi}\in H^{\infty}(\mathbb{T})\}. \] In this paper, the author gives a complete description of the Cowen set via a solution of a \(H^{\infty}\) optimization problem when \(\varphi\) is of bounded type and the Toeplitz operator \(T_{\varphi}\) on \(H^{2}(\mathbb{T})\) with symbol \(\varphi\) has finite rank selfcommutator. Reviewer: Takeaki Yamazaki (Yokohama) Cited in 1 ReviewCited in 5 Documents MSC: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 47B20 Subnormal operators, hyponormal operators, etc. 30D55 \(H^p\)-classes (MSC2000) 47A57 Linear operator methods in interpolation, moment and extension problems Keywords:Cowen sets; \(H^{\infty}\) optimization problem; Toeplitz operators; Hankel operators; hyponormal operator; bounded type; Carathéodory-Schur interpolation problem PDFBibTeX XMLCite \textit{W. Y. Lee}, J. Oper. Theory 54, No. 2, 261--267 (2005; Zbl 1100.47025)