Communications in Mathematical Analysis

Commutative Algebras of Toeplitz Operators on the Pluriharmonic Bergman Space

M. Loaiza and C. Lozano

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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

Permanent link to this document
https://projecteuclid.org/euclid.cma/1418919768

Mathematical Reviews number (MathSciNet)
MR3292972

Zentralblatt MATH identifier
1326.32015

Subjects
Primary: 31C10: Pluriharmonic and plurisubharmonic functions [See also 32U05] 31B05: Harmonic, subharmonic, superharmonic functions 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15] 32A36: Bergman spaces 47L80: Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)

Keywords
Pluriharmonic function harmonic function Toeplitz operator Bergman spaces Banach algebra

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


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