Best Approximations in a Class of Lorentz Ideals

Fang Quanlei Fang; Xia Jingbo Xia

doi:10.1007/s11785-022-01220-z

Best Approximations in a Class of Lorentz Ideals

Fang Quanlei Fang
, Xia Jingbo Xia

Mathematics

City University of New York

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We consider the family of Lorentz ideals C+p, 1 ≤ p < ∞. Let C+(0) p be the (formula presented) -closure of the collection of finite-rank operators in C+p. It is well known that C+(0) (formula presented). We show that C+(0) p is proximinal in C+p. 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
Title of host publication	Multivariable Operator Theory
Subtitle of host publication	the Jörg Eschmeier Memorial Volume
Publisher	Springer Nature
Pages	419-443
Number of pages	25
ISBN (Electronic)	9783031505355
ISBN (Print)	9783031505348
DOIs	https://doi.org/10.1007/s11785-022-01220-z
State	Published - Jan 1 2023

Keywords

Best approximation
Lorentz ideal

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10.1007/s11785-022-01220-z

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N2 - We consider the family of Lorentz ideals C+p, 1 ≤ p < ∞. Let C+(0) p be the (formula presented) -closure of the collection of finite-rank operators in C+p. It is well known that C+(0) (formula presented). We show that C+(0) p is proximinal in C+p. 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.

AB - We consider the family of Lorentz ideals C+p, 1 ≤ p < ∞. Let C+(0) p be the (formula presented) -closure of the collection of finite-rank operators in C+p. It is well known that C+(0) (formula presented). We show that C+(0) p is proximinal in C+p. 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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BT - Multivariable Operator Theory

PB - Springer Nature

ER -

Best Approximations in a Class of Lorentz Ideals

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