Abstract and Applied Analysis
Volume 2010 (2010), Article ID 426319, 14 pages
Research Article

Quasinormality and Numerical Ranges of Certain Classes of Dual Toeplitz Operators

Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 14 May 2010; Accepted 30 August 2010

Academic Editor: Stephen Clark

Copyright © 2010 Hocine Guediri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The study of dual Toeplitz operators was elaborated by Stroethoff and Zheng (2002), 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.