Zero products of toeplitz operators with n-harmonic symbols

Research output: Contribution to journalArticle

7 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 languageEnglish
Pages (from-to)43-66
Number of pages24
JournalIntegral Equations and Operator Theory
Volume57
Issue number1
DOIs
Publication statusPublished - 2007 Jan 1

Fingerprint

Toeplitz Operator
Harmonic
Zero
Continuous Extension
Polydisk
Lipschitz Continuity
Bergman Space
Unit

Keywords

  • Bergman space
  • N-Harmonic symbol
  • Polydisk
  • Toeplitz operator
  • Zero product

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis

Cite this

Zero products of toeplitz operators with n-harmonic symbols. / Choe, Boo Rim; Koo, Hyung Woon; Lee, Young Joo.

In: Integral Equations and Operator Theory, Vol. 57, No. 1, 01.01.2007, p. 43-66.

Research output: Contribution to journalArticle

@article{e1546f979220490e87ea0e479bddd510,
title = "Zero products of toeplitz operators with n-harmonic symbols",
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 Koo, {Hyung Woon} and Lee, {Young Joo}",
year = "2007",
month = "1",
day = "1",
doi = "10.1007/s00020-006-1444-2",
language = "English",
volume = "57",
pages = "43--66",
journal = "Integral Equations and Operator Theory",
issn = "0378-620X",
publisher = "Birkhauser Verlag Basel",
number = "1",

}

TY - JOUR

T1 - Zero products of toeplitz operators with n-harmonic symbols

AU - Choe, Boo Rim

AU - Koo, Hyung Woon

AU - Lee, Young Joo

PY - 2007/1/1

Y1 - 2007/1/1

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

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

U2 - 10.1007/s00020-006-1444-2

DO - 10.1007/s00020-006-1444-2

M3 - Article

VL - 57

SP - 43

EP - 66

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 1

ER -