Best Approximations in a Class of Lorentz Ideals

Quanlei Fang; Jingbo Xia

doi:10.1007/s11785-022-01220-z

Best Approximations in a Class of Lorentz Ideals

Quanlei Fang
, Jingbo Xia

Mathematics

City University of New York

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

1 Scopus citations

Abstract

We consider the family of Lorentz ideals Cp+, 1 ≤ p< ∞. Let Cp+(0) be the ‖·‖p+-closure of the collection of finite-rank operators in Cp+. It is well known that Cp+(0)≠Cp+. We show that Cp+(0) is proximinal in Cp+. We further show that a classic approximation for Hankel operators (Axler et al. in Ann Math (2) 109, 601–612, 1979) does not generalize to this new context.

Original language	English
Article number	51
Journal	Complex Analysis and Operator Theory
Volume	16
Issue number	4
DOIs	https://doi.org/10.1007/s11785-022-01220-z
State	Published - Jun 2022

Keywords

Best approximation
Lorentz ideal

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10.1007/s11785-022-01220-z

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AB - We consider the family of Lorentz ideals Cp+, 1 ≤ p< ∞. Let Cp+(0) be the ‖·‖p+-closure of the collection of finite-rank operators in Cp+. It is well known that Cp+(0)≠Cp+. We show that Cp+(0) is proximinal in Cp+. We further show that a classic approximation for Hankel operators (Axler et al. in Ann Math (2) 109, 601–612, 1979) does not generalize to this new context.

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KW - Lorentz ideal

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DO - 10.1007/s11785-022-01220-z

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ER -

Best Approximations in a Class of Lorentz Ideals

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Keywords

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