Ranks of commutators of Toeplitz operators on the harmonic Bergman space

초록

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 a parts per thousand yen 0, we also show that there are two symbols for which the corresponding Toeplitz operators induce the commutator with rank 2n exactly.

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