International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 492690, 14 pages
http://dx.doi.org/10.1155/2012/492690
Research Article

Toeplitz Operators with Essentially Radial Symbols

Roberto C. Raimondo1,2

1Division of Mathematics, Faculty of Statistical Sciences, University of Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy
2Department of Economics, University of Melbourne, Parkville, VIC 3010, Australia

Received 1 July 2011; Revised 4 October 2011; Accepted 4 October 2011

Academic Editor: Nak Cho

Copyright © 2012 Roberto C. Raimondo. 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.

Abstract

For Topelitz operators with radial symbols on the disk, there are important results that characterize boundedness, compactness, and its relation to the Berezin transform. The notion of essentially radial symbol is a natural extension, in the context of multiply-connected domains, of the notion of radial symbol on the disk. In this paper we analyze the relationship between the boundary behavior of the Berezin transform and the compactness of 𝑇 𝜙 when 𝜙 ∈ 𝐿 2 ( Ω ) is essentially radial and Ω is multiply-connected domains.