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Closed ideals of operators on the Baernstein and Schreier spaces

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Closed ideals of operators on the Baernstein and Schreier spaces. / Laustsen, Niels; Smith, James.
In: Journal of Mathematical Analysis and Applications, Vol. 546, No. 2, 129235, 15.06.2025.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Laustsen, N & Smith, J 2025, 'Closed ideals of operators on the Baernstein and Schreier spaces', Journal of Mathematical Analysis and Applications, vol. 546, no. 2, 129235. https://doi.org/10.1016/j.jmaa.2025.129235

APA

Laustsen, N., & Smith, J. (2025). Closed ideals of operators on the Baernstein and Schreier spaces. Journal of Mathematical Analysis and Applications, 546(2), Article 129235. Advance online publication. https://doi.org/10.1016/j.jmaa.2025.129235

Vancouver

Laustsen N, Smith J. Closed ideals of operators on the Baernstein and Schreier spaces. Journal of Mathematical Analysis and Applications. 2025 Jun 15;546(2):129235. Epub 2025 Jan 10. doi: 10.1016/j.jmaa.2025.129235

Author

Laustsen, Niels ; Smith, James. / Closed ideals of operators on the Baernstein and Schreier spaces. In: Journal of Mathematical Analysis and Applications. 2025 ; Vol. 546, No. 2.

Bibtex

@article{c639e0bf2ed247e996f7c22bc3301e32,
title = "Closed ideals of operators on the Baernstein and Schreier spaces",
abstract = "We study the lattice of closed ideals of bounded operators on two families of Banach spaces: the Baernstein spaces Bp for 1<p<∞ and the Schreier spaces Sp for 1≤p<∞. Our main conclusion is that there are 2 to the continuum many closed ideals that lie between the ideals of compact and  strictly singular operators on each of these spaces, and also 2 to the continuum many closed ideals that contain projections of infinite rank. Counterparts of results of Gasparis and Leung using a numerical index to distinguish the isomorphism types of subspaces spanned by subsequences of the unit vector basis for the higher-order Schreier spaces play a key role in the proofs, as does the Johnson-Schechtman technique for constructing 2 to the continuum many closed ideals of operators on a Banach space. ",
keywords = "Banach space, Baernstein space, Schreier space, bounded operator, closed operator ideal, ideal lattice, Gasparis-Leung index",
author = "Niels Laustsen and James Smith",
year = "2025",
month = jan,
day = "10",
doi = "10.1016/j.jmaa.2025.129235",
language = "English",
volume = "546",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "2",

}

RIS

TY - JOUR

T1 - Closed ideals of operators on the Baernstein and Schreier spaces

AU - Laustsen, Niels

AU - Smith, James

PY - 2025/1/10

Y1 - 2025/1/10

N2 - We study the lattice of closed ideals of bounded operators on two families of Banach spaces: the Baernstein spaces Bp for 1<p<∞ and the Schreier spaces Sp for 1≤p<∞. Our main conclusion is that there are 2 to the continuum many closed ideals that lie between the ideals of compact and  strictly singular operators on each of these spaces, and also 2 to the continuum many closed ideals that contain projections of infinite rank. Counterparts of results of Gasparis and Leung using a numerical index to distinguish the isomorphism types of subspaces spanned by subsequences of the unit vector basis for the higher-order Schreier spaces play a key role in the proofs, as does the Johnson-Schechtman technique for constructing 2 to the continuum many closed ideals of operators on a Banach space.

AB - We study the lattice of closed ideals of bounded operators on two families of Banach spaces: the Baernstein spaces Bp for 1<p<∞ and the Schreier spaces Sp for 1≤p<∞. Our main conclusion is that there are 2 to the continuum many closed ideals that lie between the ideals of compact and  strictly singular operators on each of these spaces, and also 2 to the continuum many closed ideals that contain projections of infinite rank. Counterparts of results of Gasparis and Leung using a numerical index to distinguish the isomorphism types of subspaces spanned by subsequences of the unit vector basis for the higher-order Schreier spaces play a key role in the proofs, as does the Johnson-Schechtman technique for constructing 2 to the continuum many closed ideals of operators on a Banach space.

KW - Banach space

KW - Baernstein space

KW - Schreier space

KW - bounded operator

KW - closed operator ideal

KW - ideal lattice

KW - Gasparis-Leung index

U2 - 10.1016/j.jmaa.2025.129235

DO - 10.1016/j.jmaa.2025.129235

M3 - Journal article

VL - 546

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

M1 - 129235

ER -