We study the skew-commutativity of Toeplitz operators and dual Toeplitz operators on the Bergman space of the unit disk. For bounded harmonic symbols, we characterize when two Toeplitz operators are skew-commuting. For general bounded measurable symbols, we give necessary and sufficient conditions for the skew-commutativity of dual Toeplitz operators. Our results characterize skew-commutativity in both settings and show that the conditions are more restrictive than in the commutative case.
Ma et al. (Mon,) studied this question.