On Narrow Operators from Lp into Operator Ideals

Jinghao Huang; Marat Pliev; Fedor Sukochev

doi:10.1007/s00009-022-02118-y

On Narrow Operators from L_p into Operator Ideals

Jinghao Huang^*
, Marat Pliev
, Fedor Sukochev

^*Corresponding author for this work

School of Mathematics

University of New South Wales
Russian Academy of Sciences
North Caucasus Center for Mathematical Research

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

7 Scopus citations

Abstract

It is well known that every l₂-strictly singular operator from L_p, 1 < p< ∞ to any Banach space X with an unconditional basis is narrow. In this article, we extend this result to the setting of Banach spaces without an unconditional basis. We show that if 1 ≤ p, r< ∞, then every ℓ₂-strictly singular operator T from L_p into the Schatten–von Neumann r-class C_r is narrow. This is a noncommutative complement to results in Mykhaylyuk et al. (in Israel J Math 203:81–108, 2014).

Original language	English
Article number	208
Journal	Mediterranean Journal of Mathematics
Volume	19
Issue number	5
DOIs	https://doi.org/10.1007/s00009-022-02118-y
State	Published - Oct 2022

Keywords

Narrow operators
operator ideals
ℓ-strictly singular operators

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title = "On Narrow Operators from Lp into Operator Ideals",

abstract = "It is well known that every l2-strictly singular operator from Lp, 1 < p< ∞ to any Banach space X with an unconditional basis is narrow. In this article, we extend this result to the setting of Banach spaces without an unconditional basis. We show that if 1 ≤ p, r< ∞, then every ℓ2-strictly singular operator T from Lp into the Schatten–von Neumann r-class Cr is narrow. This is a noncommutative complement to results in Mykhaylyuk et al. (in Israel J Math 203:81–108, 2014).",

keywords = "Narrow operators, operator ideals, ℓ-strictly singular operators",

author = "Jinghao Huang and Marat Pliev and Fedor Sukochev",

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T1 - On Narrow Operators from Lp into Operator Ideals

AU - Huang, Jinghao

AU - Pliev, Marat

AU - Sukochev, Fedor

PY - 2022/10

Y1 - 2022/10

N2 - It is well known that every l2-strictly singular operator from Lp, 1 < p< ∞ to any Banach space X with an unconditional basis is narrow. In this article, we extend this result to the setting of Banach spaces without an unconditional basis. We show that if 1 ≤ p, r< ∞, then every ℓ2-strictly singular operator T from Lp into the Schatten–von Neumann r-class Cr is narrow. This is a noncommutative complement to results in Mykhaylyuk et al. (in Israel J Math 203:81–108, 2014).

AB - It is well known that every l2-strictly singular operator from Lp, 1 < p< ∞ to any Banach space X with an unconditional basis is narrow. In this article, we extend this result to the setting of Banach spaces without an unconditional basis. We show that if 1 ≤ p, r< ∞, then every ℓ2-strictly singular operator T from Lp into the Schatten–von Neumann r-class Cr is narrow. This is a noncommutative complement to results in Mykhaylyuk et al. (in Israel J Math 203:81–108, 2014).

KW - Narrow operators

KW - operator ideals

KW - ℓ-strictly singular operators

UR - https://www.scopus.com/pages/publications/85137315697

U2 - 10.1007/s00009-022-02118-y

DO - 10.1007/s00009-022-02118-y

M3 - 文章

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SN - 1660-5446

VL - 19

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 5

M1 - 208

ER -

On Narrow Operators from L_p into Operator Ideals

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Keywords

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