BEREZIN TRANSFORM OF PRODUCTS OF TOEPLITZ OPERATORS ON THE HARDY SPACE

Jingbo Xia

doi:10.1090/proc/16268

BEREZIN TRANSFORM OF PRODUCTS OF TOEPLITZ OPERATORS ON THE HARDY SPACE

Jingbo Xia

Mathematics

University at Buffalo

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

Abstract

Let H²(S) be the Hardy space on the unit sphere in Cⁿ. We show that there are Toeplitz operators T_f and Tg on H²(S) such that the product T_fTg is not compact and yet ∥ T_fTgkz ∥ tends to 0 as |z| → 1. Consequently, the Berezin transform 〈T_fTgkz, kz〉 tends to 0 as |z| → 1.

Original language	English
Pages (from-to)	4269-4276
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	152
Issue number	10
DOIs	https://doi.org/10.1090/proc/16268
State	Published - Oct 2024

Keywords

Berezin transform
Toeplitz operator

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10.1090/proc/16268

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title = "BEREZIN TRANSFORM OF PRODUCTS OF TOEPLITZ OPERATORS ON THE HARDY SPACE",

abstract = "Let H2(S) be the Hardy space on the unit sphere in Cn. We show that there are Toeplitz operators Tf and Tg on H2(S) such that the product TfTg is not compact and yet ∥ TfTgkz ∥ tends to 0 as |z| → 1. Consequently, the Berezin transform 〈TfTgkz, kz〉 tends to 0 as |z| → 1.",

keywords = "Berezin transform, Toeplitz operator",

author = "Jingbo Xia",

note = "Publisher Copyright: {\textcopyright} 2024 American Mathematical Society.",

year = "2024",

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N2 - Let H2(S) be the Hardy space on the unit sphere in Cn. We show that there are Toeplitz operators Tf and Tg on H2(S) such that the product TfTg is not compact and yet ∥ TfTgkz ∥ tends to 0 as |z| → 1. Consequently, the Berezin transform 〈TfTgkz, kz〉 tends to 0 as |z| → 1.

AB - Let H2(S) be the Hardy space on the unit sphere in Cn. We show that there are Toeplitz operators Tf and Tg on H2(S) such that the product TfTg is not compact and yet ∥ TfTgkz ∥ tends to 0 as |z| → 1. Consequently, the Berezin transform 〈TfTgkz, kz〉 tends to 0 as |z| → 1.

KW - Berezin transform

KW - Toeplitz operator

UR - https://www.scopus.com/pages/publications/85203440524

U2 - 10.1090/proc/16268

DO - 10.1090/proc/16268

M3 - Article

SN - 0002-9939

VL - 152

SP - 4269

EP - 4276

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 10

ER -

BEREZIN TRANSFORM OF PRODUCTS OF TOEPLITZ OPERATORS ON THE HARDY SPACE

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Keywords

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