A remark on Toeplitz and Laurent operators acting on ℓp spaces with power weights

Oleksiy Karlovych; Eugene Shargorodsky

doi:10.1016/j.laa.2023.08.022

A remark on Toeplitz and Laurent operators acting on ℓp spaces with power weights

Oleksiy Karlovych, Eugene Shargorodsky

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Abstract

In the late 1980's, Böttcher and Silbermann asked whether the boundedness of the Toeplitz operator T(a) on the space ℓμp(Z+) implies boundedness of the Laurent operator M(a) on the space ℓ0,μp,p(Z). We give the negative answer to this question.

Original language	English
Pages (from-to)	82-92
Number of pages	11
Journal	Linear Algebra and its Applications
Volume	697
DOIs	https://doi.org/10.1016/j.laa.2023.08.022
Publication status	Published - 15 Sept 2024

Keywords

Discrete Hilbert transform
Discrete Muckenhoupt condition
Laurent operator
Power weight
Toeplitz operator
Weighted ℓ space

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10.1016/j.laa.2023.08.022

OKES16-LAA-2023-08-30Licence: CC BY

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abstract = "In the late 1980's, B{\"o}ttcher and Silbermann asked whether the boundedness of the Toeplitz operator T(a) on the space ℓμp(Z+) implies boundedness of the Laurent operator M(a) on the space ℓ0,μp,p(Z). We give the negative answer to this question.",

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AU - Karlovych, Oleksiy

AU - Shargorodsky, Eugene

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N2 - In the late 1980's, Böttcher and Silbermann asked whether the boundedness of the Toeplitz operator T(a) on the space ℓμp(Z+) implies boundedness of the Laurent operator M(a) on the space ℓ0,μp,p(Z). We give the negative answer to this question.

AB - In the late 1980's, Böttcher and Silbermann asked whether the boundedness of the Toeplitz operator T(a) on the space ℓμp(Z+) implies boundedness of the Laurent operator M(a) on the space ℓ0,μp,p(Z). We give the negative answer to this question.

KW - Discrete Hilbert transform

KW - Discrete Muckenhoupt condition

KW - Laurent operator

KW - Power weight

KW - Toeplitz operator

KW - Weighted ℓ space

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VL - 697

SP - 82

EP - 92

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

A remark on Toeplitz and Laurent operators acting on ℓp spaces with power weights

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Keywords

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