International Journal of Mathematics and Mathematical Sciences
Volume 2005 (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 Vasile Lauric. 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.