Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space
Tom 219 / 2013
Studia Mathematica 219 (2013), 163-175
MSC: Primary 47B35.
DOI: 10.4064/sm219-2-6
Streszczenie
We present here a quite unexpected result: If the product of two quasihomogeneous Toeplitz operators 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.
