Zero products of Toeplitz operators with harmonic symbols

Boorim Choe; Hyungwoon Koo

doi:10.1016/j.jfa.2005.08.007

Zero products of Toeplitz operators with harmonic symbols

Boorim Choe, Hyungwoon Koo

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

21 Citations (Scopus)

Abstract

On the Bergman space of the unit ball in Cⁿ, we solve the zero-product problem for two Toeplitz operators with harmonic symbols that have continuous extensions to (some part of) the boundary. In the case where symbols have Lipschitz continuous extensions to the boundary, we solve the zero-product problem for multiple products with the number of factors depending on the dimension n of the underlying space; the number of factors is n + 3. We also prove a local version of this result but with loss of a factor.

Original language	English
Pages (from-to)	307-334
Number of pages	28
Journal	Journal of Functional Analysis
Volume	233
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2005.08.007
Publication status	Published - 2006 Apr 15

Bibliographical note

Funding Information:
This research was supported by KOSEF (R01-2003-000-10243-0). ∗Corresponding author. E-mail addresses: [email protected] (B. Choe), [email protected] (H. Koo).

Keywords

Bergman space
Harmonic symbol
Toeplitz operator
Zero product

ASJC Scopus subject areas

Analysis

Access to Document

10.1016/j.jfa.2005.08.007

Cite this

@article{cb5e180dc8d2425ea127329e0fea4476,

title = "Zero products of Toeplitz operators with harmonic symbols",

abstract = "On the Bergman space of the unit ball in Cn, we solve the zero-product problem for two Toeplitz operators with harmonic symbols that have continuous extensions to (some part of) the boundary. In the case where symbols have Lipschitz continuous extensions to the boundary, we solve the zero-product problem for multiple products with the number of factors depending on the dimension n of the underlying space; the number of factors is n + 3. We also prove a local version of this result but with loss of a factor.",

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

author = "Boorim Choe and Hyungwoon Koo",

note = "Funding Information: This research was supported by KOSEF (R01-2003-000-10243-0). ∗Corresponding author. E-mail addresses: [email protected] (B. Choe), [email protected] (H. Koo).",

year = "2006",

month = apr,

day = "15",

doi = "10.1016/j.jfa.2005.08.007",

language = "English",

volume = "233",

pages = "307--334",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Zero products of Toeplitz operators with harmonic symbols

AU - Choe, Boorim

AU - Koo, Hyungwoon

N1 - Funding Information: This research was supported by KOSEF (R01-2003-000-10243-0). ∗Corresponding author. E-mail addresses: [email protected] (B. Choe), [email protected] (H. Koo).

PY - 2006/4/15

Y1 - 2006/4/15

N2 - On the Bergman space of the unit ball in Cn, we solve the zero-product problem for two Toeplitz operators with harmonic symbols that have continuous extensions to (some part of) the boundary. In the case where symbols have Lipschitz continuous extensions to the boundary, we solve the zero-product problem for multiple products with the number of factors depending on the dimension n of the underlying space; the number of factors is n + 3. We also prove a local version of this result but with loss of a factor.

AB - On the Bergman space of the unit ball in Cn, we solve the zero-product problem for two Toeplitz operators with harmonic symbols that have continuous extensions to (some part of) the boundary. In the case where symbols have Lipschitz continuous extensions to the boundary, we solve the zero-product problem for multiple products with the number of factors depending on the dimension n of the underlying space; the number of factors is n + 3. We also prove a local version of this result but with loss of a factor.

KW - Bergman space

KW - Harmonic symbol

KW - Toeplitz operator

KW - Zero product

UR - http://www.scopus.com/inward/record.url?scp=33645855603&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2005.08.007

DO - 10.1016/j.jfa.2005.08.007

M3 - Article

AN - SCOPUS:33645855603

SN - 0022-1236

VL - 233

SP - 307

EP - 334

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Zero products of Toeplitz operators with harmonic symbols

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this