Hankel operators and Toeplitz operators on the Bergman space
The author gives several equivalent conditions of compactness of semi- commutator \(T_{\bar fg}-T_{\bar f}T_ g\) of Toeplitz operators with bounded harmonic symbols acting on the Bergman space. As a consequence he proves Axler's conjecture (for bounded analytic functions f and g on the unit disk D the commutator \(T^*_ fT_ g- T_ gT^*_ f\) is compact iff either f or g is constant on each Gleason part P(m) except D).
Toeplitz operators with bounded harmonic symbols acting on the Bergman space
scientific article; zbMATH DE number 4111381
scientific article