Ranks of commutators of Toeplitz operators on the harmonic Bergman space (Q1946585)

The authors study the rank of the commutator of two Toeplitz operators on the harmonic Bergman space of the unit disc in dimension one. This problem has been previously studied on the Hardy space and the holomorphic Bergman space of the unit disc. The main result of the paper is that the rank of the commutator of two Toeplitz operators is always an even integer and for any even integer \(2k>0\), one can find two Toeplitz operators with bounded symbol such that the commutator has rank \(2k\).