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

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

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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. de Gruyter, 2020. p. 189-195 (De Gruyter Proceedings in Mathematics).

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

Harvard

Laustsen, NJ & White, JT 2020, 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. De Gruyter Proceedings in Mathematics, de Gruyter, pp. 189-195, 24th Conference on Banach Algebras and Applications, Winnipeg, Canada, 11/07/19. <http://10.1515/9783110602418>

APA

Laustsen, N. J., & White, J. T. (2020). 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 (pp. 189-195). (De Gruyter Proceedings in Mathematics). de Gruyter. http://10.1515/9783110602418

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. de Gruyter. 2020. p. 189-195. (De Gruyter Proceedings in Mathematics).

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. de Gruyter, 2020. pp. 189-195 (De Gruyter Proceedings in Mathematics).

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 = "2020",
month = aug,
day = "24",
language = "English",
isbn = "9783110601329",
series = "De Gruyter Proceedings in Mathematics",
publisher = "de Gruyter",
pages = "189--195",
editor = "Mahmoud Filali",
booktitle = "Proceedings of the 24th International Conference on Banach algebras and Applications",
address = "Germany",
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 - 2020/8/24

Y1 - 2020/8/24

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

SN - 9783110601329

T3 - De Gruyter Proceedings in Mathematics

SP - 189

EP - 195

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

A2 - Filali, Mahmoud

PB - de Gruyter

T2 - 24th Conference on Banach Algebras and Applications

Y2 - 11 July 2019 through 18 July 2019

ER -