Home > Research > Publications & Outputs > Subspaces that can and cannot be the kernel of ...

Electronic data

Links

View graph of relations

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/ISSNConference contribution/Paperpeer-review

Published
Publication date24/08/2020
Host publicationProceedings of the 24th International Conference on Banach algebras and Applications
EditorsMahmoud Filali
Publisherde Gruyter
Pages189-195
Number of pages6
ISBN (electronic)9783110602418
ISBN (print)9783110601329
<mark>Original language</mark>English
Event24th Conference on Banach Algebras and Applications - University of Manitoba, Winnipeg, Canada
Duration: 11/07/201918/07/2019
https://server.math.umanitoba.ca/~banach2019/

Conference

Conference24th Conference on Banach Algebras and Applications
Country/TerritoryCanada
CityWinnipeg
Period11/07/1918/07/19
Internet address

Publication series

NameDe Gruyter Proceedings in Mathematics
PublisherDe Gruyter
ISSN (Print)2942-4801
ISSN (electronic)2942-4828

Conference

Conference24th Conference on Banach Algebras and Applications
Country/TerritoryCanada
CityWinnipeg
Period11/07/1918/07/19
Internet address

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’s non-separable, reflexive Banach spaces with few operators.

Bibliographic note

This paper has been independently refereed prior to acceptance