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  • acceptedPAMSmarch2023

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A surjective summation operator with no Lipschitz right inverse

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

Forthcoming

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A surjective summation operator with no Lipschitz right inverse. / Laustsen, Niels; Messerschmidt, Miek; Wortel, Marten.
In: Proceedings of the American Mathematical Society, 30.03.2023.

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

Harvard

Laustsen, N, Messerschmidt, M & Wortel, M 2023, 'A surjective summation operator with no Lipschitz right inverse', Proceedings of the American Mathematical Society.

APA

Laustsen, N., Messerschmidt, M., & Wortel, M. (in press). A surjective summation operator with no Lipschitz right inverse. Proceedings of the American Mathematical Society.

Vancouver

Laustsen N, Messerschmidt M, Wortel M. A surjective summation operator with no Lipschitz right inverse. Proceedings of the American Mathematical Society. 2023 Mar 30.

Author

Laustsen, Niels ; Messerschmidt, Miek ; Wortel, Marten. / A surjective summation operator with no Lipschitz right inverse. In: Proceedings of the American Mathematical Society. 2023.

Bibtex

@article{1d692bc3aea94d1388a6908b116fe8b8,
title = "A surjective summation operator with no Lipschitz right inverse",
abstract = "We show that there exists a Banach space X which contains closed subspaces Y and Z with Y+Z=X such that the associated surjective summation operator Σ: Y×Z→X defined by Σ(y,z)= y+z for y∈Y and z∈Z has no Lipschitz right inverse.",
keywords = "Banach space, summation operator, surjection, right inverse, Lipschitz map",
author = "Niels Laustsen and Miek Messerschmidt and Marten Wortel",
year = "2023",
month = mar,
day = "30",
language = "English",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",

}

RIS

TY - JOUR

T1 - A surjective summation operator with no Lipschitz right inverse

AU - Laustsen, Niels

AU - Messerschmidt, Miek

AU - Wortel, Marten

PY - 2023/3/30

Y1 - 2023/3/30

N2 - We show that there exists a Banach space X which contains closed subspaces Y and Z with Y+Z=X such that the associated surjective summation operator Σ: Y×Z→X defined by Σ(y,z)= y+z for y∈Y and z∈Z has no Lipschitz right inverse.

AB - We show that there exists a Banach space X which contains closed subspaces Y and Z with Y+Z=X such that the associated surjective summation operator Σ: Y×Z→X defined by Σ(y,z)= y+z for y∈Y and z∈Z has no Lipschitz right inverse.

KW - Banach space

KW - summation operator

KW - surjection

KW - right inverse

KW - Lipschitz map

M3 - Journal article

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

ER -