Commutants of analytic Toeplitz operators on the harmonic Bergman space

Rim Choe Boo; Joo Lee Young

doi:10.1007/s00020-004-1338-0

Commutants of analytic Toeplitz operators on the harmonic Bergman space

Rim Choe Boo, Joo Lee Young

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

We study the commuting problem for Toeplitz operators on the harmonic Bergman space of the unit disk. We show that an analytic Toeplitz operator and a co-analytic Toeplitz operator with certain noncyclicity hypothesis can commute only when one of their symbols is constant. We also obtain analogous results for semi-commutants.

Original language	English
Pages (from-to)	559-564
Number of pages	6
Journal	Integral Equations and Operator Theory
Volume	50
Issue number	4
DOIs	https://doi.org/10.1007/s00020-004-1338-0
Publication status	Published - 2004 Dec

Keywords

Commutant
Harmonic Bergman space
Toeplitz operator

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-004-1338-0

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abstract = "We study the commuting problem for Toeplitz operators on the harmonic Bergman space of the unit disk. We show that an analytic Toeplitz operator and a co-analytic Toeplitz operator with certain noncyclicity hypothesis can commute only when one of their symbols is constant. We also obtain analogous results for semi-commutants.",

keywords = "Commutant, Harmonic Bergman space, Toeplitz operator",

author = "Boo, {Rim Choe} and Young, {Joo Lee}",

note = "Funding Information: The research was supported by KOSEF(R01-2003-000-10243-0).",

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AU - Boo, Rim Choe

AU - Young, Joo Lee

N1 - Funding Information: The research was supported by KOSEF(R01-2003-000-10243-0).

PY - 2004/12

Y1 - 2004/12

N2 - We study the commuting problem for Toeplitz operators on the harmonic Bergman space of the unit disk. We show that an analytic Toeplitz operator and a co-analytic Toeplitz operator with certain noncyclicity hypothesis can commute only when one of their symbols is constant. We also obtain analogous results for semi-commutants.

AB - We study the commuting problem for Toeplitz operators on the harmonic Bergman space of the unit disk. We show that an analytic Toeplitz operator and a co-analytic Toeplitz operator with certain noncyclicity hypothesis can commute only when one of their symbols is constant. We also obtain analogous results for semi-commutants.

KW - Commutant

KW - Harmonic Bergman space

KW - Toeplitz operator

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JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 4

ER -

Commutants of analytic Toeplitz operators on the harmonic Bergman space

Abstract

Keywords

ASJC Scopus subject areas

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