Quasinormality and numerical ranges of certain classes of dual Toeplitz operators (Q610864)

Summary: The study of dual Toeplitz operators was elaborated by \textit{K.\,Stroethoff} and \textit{D.-C.\thinspace Zheng} [``Algebraic and spectral properties of dual Toeplitz operators'', Trans.\ Am.\ Math.\ Soc.\ 354, No.\,6, 2495--2520 (2002; Zbl 0996.47036)], where various corresponding algebraic and spectral properties were established. In this paper, we characterize numerical ranges of certain classes of dual Toeplitz operators. Moreover, we introduce the analog of Halmos' fifth classification problem for quasinormal dual Toeplitz operators. In particular, we show that there are no quasinormal dual Toeplitz operators with bounded analytic or coanalytic symbols which are not normal.