Finite rank commutators of Toeplitz operators on the bidisk
Volume 209 / 2012
Studia Mathematica 209 (2012), 189-201
MSC: Primary 47B35; Secondary 32A35.
DOI: 10.4064/sm209-2-6
Abstract
We study some algebraic properties of commutators of Toeplitz operators on the Hardy space of the bidisk. First, for two symbols where one is arbitrary and the other is (co-)analytic with respect to one fixed variable, we show that there is no nontrivial finite rank commutator. Also, for two symbols with separated variables, we prove that there is no nontrivial finite rank commutator or compact commutator in certain cases.
