Commuting Toeplitz operators on the polydisk

Boo Rim Choe; Hyungwoon Koo; Young Joo Lee

doi:10.1090/S0002-9947-03-03430-5

Commuting Toeplitz operators on the polydisk

Boo Rim Choe, Hyungwoon Koo, Young Joo Lee

Department of Mathematics

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

29 Citations (Scopus)

Abstract

We obtain characterizations of (essentially) commuting Toeplitz operators with pluriharmonic symbols on the Bergman space of the polydisk. We show that commuting and essential commuting properties are the same for dimensions bigger than 2, while they are not for dimensions less than or equal to 2. Also, the corresponding results for semi-commutators are obtained.

Original language	English
Pages (from-to)	1727-1749
Number of pages	23
Journal	Transactions of the American Mathematical Society
Volume	356
Issue number	5
DOIs	https://doi.org/10.1090/S0002-9947-03-03430-5
Publication status	Published - 2004 May

Keywords

Bergman space
N-harmonic function
Toeplitz operator

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-03-03430-5

Cite this

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abstract = "We obtain characterizations of (essentially) commuting Toeplitz operators with pluriharmonic symbols on the Bergman space of the polydisk. We show that commuting and essential commuting properties are the same for dimensions bigger than 2, while they are not for dimensions less than or equal to 2. Also, the corresponding results for semi-commutators are obtained.",

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AU - Koo, Hyungwoon

AU - Lee, Young Joo

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N2 - We obtain characterizations of (essentially) commuting Toeplitz operators with pluriharmonic symbols on the Bergman space of the polydisk. We show that commuting and essential commuting properties are the same for dimensions bigger than 2, while they are not for dimensions less than or equal to 2. Also, the corresponding results for semi-commutators are obtained.

AB - We obtain characterizations of (essentially) commuting Toeplitz operators with pluriharmonic symbols on the Bergman space of the polydisk. We show that commuting and essential commuting properties are the same for dimensions bigger than 2, while they are not for dimensions less than or equal to 2. Also, the corresponding results for semi-commutators are obtained.

KW - Bergman space

KW - N-harmonic function

KW - Toeplitz operator

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ER -

Commuting Toeplitz operators on the polydisk

Abstract

Keywords

ASJC Scopus subject areas

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