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  • LLechnerMuellerJFAacceptedFeb2018

    Rights statement: This is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, 275, 11, 2018 DOI: 10.1016/j.jfa.2018.02.010

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Factorization of the identity through operators with large diagonal

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

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Factorization of the identity through operators with large diagonal. / Laustsen, Niels Jakob; Lechner, Richard; Mueller, Paul.
In: Journal of Functional Analysis, Vol. 275, No. 11, 01.12.2018, p. 3169-3207.

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

Harvard

Laustsen, NJ, Lechner, R & Mueller, P 2018, 'Factorization of the identity through operators with large diagonal', Journal of Functional Analysis, vol. 275, no. 11, pp. 3169-3207. https://doi.org/10.1016/j.jfa.2018.02.010

APA

Laustsen, N. J., Lechner, R., & Mueller, P. (2018). Factorization of the identity through operators with large diagonal. Journal of Functional Analysis, 275(11), 3169-3207. https://doi.org/10.1016/j.jfa.2018.02.010

Vancouver

Laustsen NJ, Lechner R, Mueller P. Factorization of the identity through operators with large diagonal. Journal of Functional Analysis. 2018 Dec 1;275(11):3169-3207. Epub 2018 Mar 2. doi: 10.1016/j.jfa.2018.02.010

Author

Laustsen, Niels Jakob ; Lechner, Richard ; Mueller, Paul. / Factorization of the identity through operators with large diagonal. In: Journal of Functional Analysis. 2018 ; Vol. 275, No. 11. pp. 3169-3207.

Bibtex

@article{1b8bb7040c494c89a3ca530844300bd8,
title = "Factorization of the identity through operators with large diagonal",
abstract = "Given a Banach space X with an unconditional basis, we consider the following question: does the identity operator on X factor through every operator on X with large diagonal relative to the unconditional basis? We show that on Gowers' unconditional Banach space, there exists an operator for which the answer to the question is negative. By contrast, for any operator on the mixed-norm Hardy spaces Hp(Hq), where 1≤p,q<∞, with the bi-parameter Haar system, this problem always has a positive solution. The spaces Lp, 1Studia Math. 1979].",
keywords = "Factorization of operators, mixed-norm Hardy space, Fredholm theory, Gowers-Maurey space",
author = "Laustsen, {Niels Jakob} and Richard Lechner and Paul Mueller",
note = "This is the author{\textquoteright}s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, 275, 11, 2018 DOI: 10.1016/j.jfa.2018.02.010",
year = "2018",
month = dec,
day = "1",
doi = "10.1016/j.jfa.2018.02.010",
language = "English",
volume = "275",
pages = "3169--3207",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "11",

}

RIS

TY - JOUR

T1 - Factorization of the identity through operators with large diagonal

AU - Laustsen, Niels Jakob

AU - Lechner, Richard

AU - Mueller, Paul

N1 - This is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, 275, 11, 2018 DOI: 10.1016/j.jfa.2018.02.010

PY - 2018/12/1

Y1 - 2018/12/1

N2 - Given a Banach space X with an unconditional basis, we consider the following question: does the identity operator on X factor through every operator on X with large diagonal relative to the unconditional basis? We show that on Gowers' unconditional Banach space, there exists an operator for which the answer to the question is negative. By contrast, for any operator on the mixed-norm Hardy spaces Hp(Hq), where 1≤p,q<∞, with the bi-parameter Haar system, this problem always has a positive solution. The spaces Lp, 1Studia Math. 1979].

AB - Given a Banach space X with an unconditional basis, we consider the following question: does the identity operator on X factor through every operator on X with large diagonal relative to the unconditional basis? We show that on Gowers' unconditional Banach space, there exists an operator for which the answer to the question is negative. By contrast, for any operator on the mixed-norm Hardy spaces Hp(Hq), where 1≤p,q<∞, with the bi-parameter Haar system, this problem always has a positive solution. The spaces Lp, 1Studia Math. 1979].

KW - Factorization of operators

KW - mixed-norm Hardy space

KW - Fredholm theory

KW - Gowers-Maurey space

U2 - 10.1016/j.jfa.2018.02.010

DO - 10.1016/j.jfa.2018.02.010

M3 - Journal article

VL - 275

SP - 3169

EP - 3207

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 11

ER -