International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 6, Pages 823-835
doi:10.1155/IJMMS.2005.823

On a weighted Toeplitz operator and its commutant

Abstract

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.