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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 6, Pages 823-835

On a weighted Toeplitz operator and its commutant

Department of Mathematics, Florida A&M University, Tallahassee 32307, FL, USA

Received 14 July 2004; Revised 28 February 2005

Copyright © 2005 Hindawi Publishing Corporation. 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.


We study the structure of a class of weighted Toeplitz operators and obtain a description of the commutant of each operator in this class. We make some progress towards proving that the only operator in the commutant which is not a scalar multiple of the identity operator and which commutes with a nonzero compact operator is zero. The proof of the main statement relies on a conjecture which is left as an open problem.