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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-2-6,
author = {Young Joo Lee},
title = {Finite rank commutators of Toeplitz operators on the bidisk},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {189-201},
zbl = {1264.47029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-2-6}
}
Young Joo Lee. Finite rank commutators of Toeplitz operators on the bidisk. Studia Mathematica, Tome 209 (2012) pp. 189-201. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-2-6/