Blackadar, B., Farah, I. and Karagila, A. orcid.org/0000-0003-1289-0904 (2024) Hilbert spaces without the Countable Axiom of Choice. Munster Journal of Mathematics. ISSN 1867-5778
Abstract
We study elementary properties of Hilbert spaces and bounded operators in the absence of any form of the Axiom of Choice. A surprising amount of the theory continues to hold, sometimes with modified proofs, but there are some interesting surprises. It turns out there is a much greater variety of Hilbert spaces. We also obtain some new and potentially interesting types of cardinals and relations between them.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Münster Journal of Mathematics 2024. This is an author produced version of an article published in Münster Journal of Mathematics. Uploaded in with permission from the publisher. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 04 Oct 2024 13:29 |
Last Modified: | 28 Nov 2024 15:41 |
Published Version: | https://www.uni-muenster.de/FB10/mjm/acc.html |
Status: | Published online |
Publisher: | Mathematical Institutes of the Universität Münster |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:216587 |