Commutative algebras of Toeplitz operators on the pluriharmonic Bergman space (Q2517055)

The paper is devoted to the study of Toeplitz operators on weighted pluriharmonic Bergman spaces over the unit ball in \({\mathbb C}^n\). It is shown that there exist commutative Banach algebras generated by Toeplitz operators, which are not \(C^*\)-algebras. These algebras are generated by Toeplitz operators with so-called \(k\)-quasi-homogeneous symbols. This class of symbols was studied earlier by \textit{N. Vasilevski} [Integral Equations Oper. Theory 66, No. 1, 141--152 (2010; Zbl 1216.47050)].