Commutative Algebras of Toeplitz Operators on the Pluriharmonic Bergman Space

Abstract

We study Toeplitz operators acting on the weighted pluriharmonic Bergman space on the unit ball, denoted here by $b_{λ}^2({\mathbb B}^n)$. We prove that, besides the C*-algebra generated by Toeplitz operators with radial symbols, there are commutative Banach algebras generated by Toeplitz operators. These Banach algebras are generated by Toeplitz operators with k-quasi-radial and k-quasi-homogeneous symbols.