We study the rank of commutators of two Toeplitz operators on the harmonic Bergman space of the unit disk. We first show that the commutator of any two Toeplitz operators with general symbols can't have an odd rank. But, given any integer n ≥ 0, we also show that there are two symbols for which the corresponding Toeplitz operators induce the commutator with rank 2n exactly.
Bibliographical noteFunding Information:
The first author was supported in part by ZJNSFC (No. Y6110260), NSFC (No. 11201274) and Tianyuan Foundation of China (No. 11126259) and the second author is support by NRF of Korea (2012R1A1A2000705). Also, the third author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012-0001416).
- Toeplitz operator
- finite rank
- harmonic Bergman space
ASJC Scopus subject areas
- Algebra and Number Theory