Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space
Volume 219 / 2013
Studia Mathematica 219 (2013), 163-175
MSC: Primary 47B35.
DOI: 10.4064/sm219-2-6
Abstract
We present here a quite unexpected result: If the product of two quasihomogeneous Toeplitz operators $T_fT_g$ on the harmonic Bergman space is equal to a Toeplitz operator $T_h$, then the product $T_gT_f$ is also the Toeplitz operator $T_h$, and hence $T_f$ commutes with $T_g$. From this we give necessary and sufficient conditions for the product of two Toeplitz operators, one quasihomogeneous and the other monomial, to be a Toeplitz operator.
