## Communications in Mathematical Analysis

### 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.

#### Article information

Source
Commun. Math. Anal., Volume 17, Number 2 (2014), 239-252.

Dates
First available in Project Euclid: 18 December 2014

https://projecteuclid.org/euclid.cma/1418919768

Mathematical Reviews number (MathSciNet)
MR3292972

Zentralblatt MATH identifier
1326.32015

#### Citation

Loaiza , M.; Lozano, C. Commutative Algebras of Toeplitz Operators on the Pluriharmonic Bergman Space. Commun. Math. Anal. 17 (2014), no. 2, 239--252. https://projecteuclid.org/euclid.cma/1418919768