Banach Journal of Mathematical Analysis

Toeplitz operators on weighted pluriharmonic Bergman space

Linghui Kong and Yufeng Lu

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Abstract

In this article, we consider some algebraic properties of Toeplitz operators on weighted pluriharmonic Bergman space on the unit ball. We characterize the commutants of Toeplitz operators whose symbols are certain separately radial functions or holomorphic monomials, and then give a partial answer to the finite-rank product problem of Toeplitz operators.

Article information

Source
Banach J. Math. Anal., Volume 12, Number 2 (2018), 439-455.

Dates
Received: 23 April 2017
Accepted: 28 August 2017
First available in Project Euclid: 18 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1516244456

Digital Object Identifier
doi:10.1215/17358787-2017-0055

Mathematical Reviews number (MathSciNet)
MR3779722

Zentralblatt MATH identifier
06873509

Subjects
Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Secondary: 47B38: Operators on function spaces (general)

Keywords
Toeplitz operator commutant finite-rank product pluriharmonic Bergman space

Citation

Kong, Linghui; Lu, Yufeng. Toeplitz operators on weighted pluriharmonic Bergman space. Banach J. Math. Anal. 12 (2018), no. 2, 439--455. doi:10.1215/17358787-2017-0055. https://projecteuclid.org/euclid.bjma/1516244456


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