Zero products of toeplitz operators with n-harmonic symbols

Boo Rim Choe; Hyungwoon Koo; Young Joo Lee

doi:10.1007/s00020-006-1444-2

Zero products of toeplitz operators with n-harmonic symbols

Boo Rim Choe, Hyungwoon Koo, Young Joo Lee

Department of Mathematics

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

9 Citations (Scopus)

Abstract

On the Bergman space of the unit polydisk in the complex n-space, we solve the zero-product problem for two Toeplitz operators with n-harmonic symbols that have local continuous extension property up to the distinguished boundary. In the case where symbols have additional Lipschitz continuity up to the whole distinguished boundary, we solve the zero-product problem for products with four factors. We also prove a local version of this result for products with three factors.

Original language	English
Pages (from-to)	43-66
Number of pages	24
Journal	Integral Equations and Operator Theory
Volume	57
Issue number	1
DOIs	https://doi.org/10.1007/s00020-006-1444-2
Publication status	Published - 2007 Jan

Keywords

Bergman space
N-Harmonic symbol
Polydisk
Toeplitz operator
Zero product

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-006-1444-2

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abstract = "On the Bergman space of the unit polydisk in the complex n-space, we solve the zero-product problem for two Toeplitz operators with n-harmonic symbols that have local continuous extension property up to the distinguished boundary. In the case where symbols have additional Lipschitz continuity up to the whole distinguished boundary, we solve the zero-product problem for products with four factors. We also prove a local version of this result for products with three factors.",

keywords = "Bergman space, N-Harmonic symbol, Polydisk, Toeplitz operator, Zero product",

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

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

year = "2007",

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doi = "10.1007/s00020-006-1444-2",

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AU - Choe, Boo Rim

AU - Koo, Hyungwoon

AU - Lee, Young Joo

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

PY - 2007/1

Y1 - 2007/1

N2 - On the Bergman space of the unit polydisk in the complex n-space, we solve the zero-product problem for two Toeplitz operators with n-harmonic symbols that have local continuous extension property up to the distinguished boundary. In the case where symbols have additional Lipschitz continuity up to the whole distinguished boundary, we solve the zero-product problem for products with four factors. We also prove a local version of this result for products with three factors.

AB - On the Bergman space of the unit polydisk in the complex n-space, we solve the zero-product problem for two Toeplitz operators with n-harmonic symbols that have local continuous extension property up to the distinguished boundary. In the case where symbols have additional Lipschitz continuity up to the whole distinguished boundary, we solve the zero-product problem for products with four factors. We also prove a local version of this result for products with three factors.

KW - Bergman space

KW - N-Harmonic symbol

KW - Polydisk

KW - Toeplitz operator

KW - Zero product

UR - http://www.scopus.com/inward/record.url?scp=33846968855&partnerID=8YFLogxK

U2 - 10.1007/s00020-006-1444-2

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M3 - Article

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JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 1

ER -

Zero products of toeplitz operators with n-harmonic symbols

Abstract

Keywords

ASJC Scopus subject areas

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