Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball

Abstract EN

We extend the known results on commutative Banach algebras generated by Toeplitz operators with radial quasi-homogeneous symbols on the two-dimensional unit ball.

Spherical coordinates previously used hid a possibility to detect an essentially wider class of symbols that can generate commutative Banach Toeplitz operator algebras.

We characterize these new algebras describing their properties and, under a certain extra condition, construct the corresponding Gelfand theory.