×

Cowen sets for Toeplitz operators with finite rank selfcommutators. (English) Zbl 1100.47025

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.

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
PDFBibTeX XMLCite