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Subspaces that can and cannot be the kernel of a bounded operator on a Banach space

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Subspaces that can and cannot be the kernel of a bounded operator on a Banach space. / Laustsen, Niels Jakob; White, Jared T.

Proceedings of the 24th International Conference on Banach algebras and Applications. ed. / Mahmoud Filali. 2018.

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNConference contribution/Paperpeer-review

Harvard

Laustsen, NJ & White, JT 2018, Subspaces that can and cannot be the kernel of a bounded operator on a Banach space. in M Filali (ed.), Proceedings of the 24th International Conference on Banach algebras and Applications. 24th Conference on Banach Algebras and Applications, Winnipeg, Canada, 11/07/19.

APA

Laustsen, N. J., & White, J. T. (Accepted/In press). Subspaces that can and cannot be the kernel of a bounded operator on a Banach space. In M. Filali (Ed.), Proceedings of the 24th International Conference on Banach algebras and Applications

Vancouver

Laustsen NJ, White JT. Subspaces that can and cannot be the kernel of a bounded operator on a Banach space. In Filali M, editor, Proceedings of the 24th International Conference on Banach algebras and Applications. 2018

Author

Laustsen, Niels Jakob ; White, Jared T. / Subspaces that can and cannot be the kernel of a bounded operator on a Banach space. Proceedings of the 24th International Conference on Banach algebras and Applications. editor / Mahmoud Filali. 2018.

Bibtex

@inproceedings{3ab9d2bacfb7447d833ba36a4c833402,
title = "Subspaces that can and cannot be the kernel of a bounded operator on a Banach space",
abstract = "Given a Banach space E, we ask which closed subspaces may be realised as the kernel of a bounded operator E→E. We prove some positive results which imply in particular that when E is separable every closed subspace is a kernel. Moreover, we show that there exists a Banach space E which contains a closed subspace that cannot be realised as the kernel of any bounded operator on E. This implies that the Banach algebra B(E) of bounded operators on E fails to be weak*-topologically left Noetherian in the sense of (JT White, Left Ideals of Banach Algebras and Dual Banach Algebras, preprint, 2018). The Banach space E that we use is the dual of one of Wark{\textquoteright}s non-separable, reflexive Banach spaces with few operators. ",
keywords = "Banach space, bounded operator, kernel, dual Banach algebra, weak*-closed ideal, Noetherian",
author = "Laustsen, {Niels Jakob} and White, {Jared T}",
note = "This paper has been independently refereed prior to acceptance ; 24th Conference on Banach Algebras and Applications ; Conference date: 11-07-2019 Through 18-07-2019",
year = "2018",
month = nov,
day = "17",
language = "English",
editor = "Mahmoud Filali",
booktitle = "Proceedings of the 24th International Conference on Banach algebras and Applications",
url = "https://server.math.umanitoba.ca/~banach2019/",

}

RIS

TY - GEN

T1 - Subspaces that can and cannot be the kernel of a bounded operator on a Banach space

AU - Laustsen, Niels Jakob

AU - White, Jared T

N1 - This paper has been independently refereed prior to acceptance

PY - 2018/11/17

Y1 - 2018/11/17

N2 - Given a Banach space E, we ask which closed subspaces may be realised as the kernel of a bounded operator E→E. We prove some positive results which imply in particular that when E is separable every closed subspace is a kernel. Moreover, we show that there exists a Banach space E which contains a closed subspace that cannot be realised as the kernel of any bounded operator on E. This implies that the Banach algebra B(E) of bounded operators on E fails to be weak*-topologically left Noetherian in the sense of (JT White, Left Ideals of Banach Algebras and Dual Banach Algebras, preprint, 2018). The Banach space E that we use is the dual of one of Wark’s non-separable, reflexive Banach spaces with few operators.

AB - Given a Banach space E, we ask which closed subspaces may be realised as the kernel of a bounded operator E→E. We prove some positive results which imply in particular that when E is separable every closed subspace is a kernel. Moreover, we show that there exists a Banach space E which contains a closed subspace that cannot be realised as the kernel of any bounded operator on E. This implies that the Banach algebra B(E) of bounded operators on E fails to be weak*-topologically left Noetherian in the sense of (JT White, Left Ideals of Banach Algebras and Dual Banach Algebras, preprint, 2018). The Banach space E that we use is the dual of one of Wark’s non-separable, reflexive Banach spaces with few operators.

KW - Banach space

KW - bounded operator

KW - kernel

KW - dual Banach algebra

KW - weak-closed ideal

KW - Noetherian

M3 - Conference contribution/Paper

BT - Proceedings of the 24th International Conference on Banach algebras and Applications

A2 - Filali, Mahmoud

T2 - 24th Conference on Banach Algebras and Applications

Y2 - 11 July 2019 through 18 July 2019

ER -