Finite rank product theorems for Toeplitz operators on the half-space

Boo Rim Choe; Hyungwoon Koo; Kyesook Nam

doi:10.2969/jmsj/06130885

Finite rank product theorems for Toeplitz operators on the half-space

Boo Rim Choe, Hyungwoon Koo, Kyesook Nam

Department of Mathematics

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

2 Citations (Scopus)

Abstract

On the harmonic Bergman space of the half space in Rⁿ, we show that if the product of two or more Toeplitz operators with harmonic symbols that have certain boundary smoothness has finite rank, then one of the symbols must be identically 0. Our methods require the number of factors in the product to depend on the dimension n.

Original language	English
Pages (from-to)	885-919
Number of pages	35
Journal	Journal of the Mathematical Society of Japan
Volume	61
Issue number	3
DOIs	https://doi.org/10.2969/jmsj/06130885
Publication status	Published - 2009 Jul

Keywords

Half-space
Harmonic Bergman space
Toeplitz operator
Zero product

ASJC Scopus subject areas

Mathematics(all)

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10.2969/jmsj/06130885

Cite this

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abstract = "On the harmonic Bergman space of the half space in Rn, we show that if the product of two or more Toeplitz operators with harmonic symbols that have certain boundary smoothness has finite rank, then one of the symbols must be identically 0. Our methods require the number of factors in the product to depend on the dimension n.",

keywords = "Half-space, Harmonic Bergman space, Toeplitz operator, Zero product",

author = "Choe, {Boo Rim} and Hyungwoon Koo and Kyesook Nam",

year = "2009",

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AU - Nam, Kyesook

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N2 - On the harmonic Bergman space of the half space in Rn, we show that if the product of two or more Toeplitz operators with harmonic symbols that have certain boundary smoothness has finite rank, then one of the symbols must be identically 0. Our methods require the number of factors in the product to depend on the dimension n.

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KW - Harmonic Bergman space

KW - Toeplitz operator

KW - Zero product

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Finite rank product theorems for Toeplitz operators on the half-space

Abstract

Keywords

ASJC Scopus subject areas

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