Finite sums of Toeplitz products on the polydisk

Boo Rim Choe; Hyungwoon Koo; Young Joo Lee

doi:10.1007/s11118-009-9133-9

Finite sums of Toeplitz products on the polydisk

Boo Rim Choe, Hyungwoon Koo, Young Joo Lee

Department of Mathematics

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

7 Citations (Scopus)

Abstract

On the Bergman space of the unit polydisk, we study a class of operators which contains sums of finitely many Toeplitz products with pluriharmonic symbols. We give characterizations of when an operator in that class has finite rank or is compact. As one of applications we show that sums of a certain number, depending on and increasing with the dimension, of semicommutators of Toeplitz operators with pluriharmonic symbols cannot be compact without being the zero operator.

Original language	English
Pages (from-to)	227-255
Number of pages	29
Journal	Potential Analysis
Volume	31
Issue number	3
DOIs	https://doi.org/10.1007/s11118-009-9133-9
Publication status	Published - 2009 Sept

Keywords

Bergman space
Finite rank operators
Polydisk
Toeplitz operators

ASJC Scopus subject areas

Analysis

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10.1007/s11118-009-9133-9

Cite this

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title = "Finite sums of Toeplitz products on the polydisk",

abstract = "On the Bergman space of the unit polydisk, we study a class of operators which contains sums of finitely many Toeplitz products with pluriharmonic symbols. We give characterizations of when an operator in that class has finite rank or is compact. As one of applications we show that sums of a certain number, depending on and increasing with the dimension, of semicommutators of Toeplitz operators with pluriharmonic symbols cannot be compact without being the zero operator.",

keywords = "Bergman space, Finite rank operators, Polydisk, Toeplitz operators",

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

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doi = "10.1007/s11118-009-9133-9",

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AU - Choe, Boo Rim

AU - Koo, Hyungwoon

AU - Lee, Young Joo

N1 - Funding Information: The first two authors were supported by the Korea Science and Engineering Foundation Grant funded by the Korean Government (KOSEF R01-2008-000-20206-0) and the third author was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-313-C00034).

PY - 2009/9

Y1 - 2009/9

N2 - On the Bergman space of the unit polydisk, we study a class of operators which contains sums of finitely many Toeplitz products with pluriharmonic symbols. We give characterizations of when an operator in that class has finite rank or is compact. As one of applications we show that sums of a certain number, depending on and increasing with the dimension, of semicommutators of Toeplitz operators with pluriharmonic symbols cannot be compact without being the zero operator.

AB - On the Bergman space of the unit polydisk, we study a class of operators which contains sums of finitely many Toeplitz products with pluriharmonic symbols. We give characterizations of when an operator in that class has finite rank or is compact. As one of applications we show that sums of a certain number, depending on and increasing with the dimension, of semicommutators of Toeplitz operators with pluriharmonic symbols cannot be compact without being the zero operator.

KW - Bergman space

KW - Finite rank operators

KW - Polydisk

KW - Toeplitz operators

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Finite sums of Toeplitz products on the polydisk

Abstract

Keywords

ASJC Scopus subject areas

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