Binormal Toeplitz operators on the Hardy space

Caixing Gu; Dong O. Kang; Eungil Ko; Ji Eun Lee

doi:10.1142/S0129167X19500010

Binormal Toeplitz operators on the Hardy space

Caixing Gu, Dong O. Kang, Eungil Ko, Ji Eun Lee

Department of Mathematics

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

Abstract

We characterize binormal Toeplitz operators with analytic, or, coanalytic symbol functions. Furthermore, for a large class of nonanalytic, noncoanalytic Toeplitz operators which include Toeplitz operators with trigonometric or rational symbols, we prove that those Toeplitz operators are binormal if and only if they are normal. Some of the historically important examples of Toeplitz operators in the paper show that our problem is subtle and the above result is sharp.

Original language	English
Article number	1950001
Journal	International Journal of Mathematics
Volume	30
Issue number	1
DOIs	https://doi.org/10.1142/S0129167X19500010
State	Published - 1 Jan 2019

Bibliographical note

Funding Information:
The second-named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015R1C1A1A01053837). The third-named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1D1A1B03931937). The last-named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2016R1A2B4007035).

Publisher Copyright:
© 2019 World Scientific Publishing Company.

Keywords

Toeplitz operator
binormal operator
model space

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10.1142/S0129167X19500010

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abstract = "We characterize binormal Toeplitz operators with analytic, or, coanalytic symbol functions. Furthermore, for a large class of nonanalytic, noncoanalytic Toeplitz operators which include Toeplitz operators with trigonometric or rational symbols, we prove that those Toeplitz operators are binormal if and only if they are normal. Some of the historically important examples of Toeplitz operators in the paper show that our problem is subtle and the above result is sharp.",

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author = "Caixing Gu and Kang, {Dong O.} and Eungil Ko and Lee, {Ji Eun}",

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AU - Ko, Eungil

AU - Lee, Ji Eun

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N2 - We characterize binormal Toeplitz operators with analytic, or, coanalytic symbol functions. Furthermore, for a large class of nonanalytic, noncoanalytic Toeplitz operators which include Toeplitz operators with trigonometric or rational symbols, we prove that those Toeplitz operators are binormal if and only if they are normal. Some of the historically important examples of Toeplitz operators in the paper show that our problem is subtle and the above result is sharp.

AB - We characterize binormal Toeplitz operators with analytic, or, coanalytic symbol functions. Furthermore, for a large class of nonanalytic, noncoanalytic Toeplitz operators which include Toeplitz operators with trigonometric or rational symbols, we prove that those Toeplitz operators are binormal if and only if they are normal. Some of the historically important examples of Toeplitz operators in the paper show that our problem is subtle and the above result is sharp.

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Binormal Toeplitz operators on the Hardy space

Abstract

Bibliographical note

Keywords

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