Article contents
Lattice isomorphisms between projection lattices of von Neumann algebras
Published online by Cambridge University Press: 13 November 2020
Abstract
Generalizing von Neumann’s result on type II
$_1$
von Neumann algebras, I characterise lattice isomorphisms between projection lattices of arbitrary von Neumann algebras by means of ring isomorphisms between the algebras of locally measurable operators. Moreover, I give a complete description of ring isomorphisms of locally measurable operator algebras when the von Neumann algebras are without type II direct summands.
- Type
- Analysis
- Information
- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Copyright
- © The Author(s), 2020. Published by Cambridge University Press
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20201119143046923-0262:S2050509420000535:S2050509420000535_inline2.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20201119143046923-0262:S2050509420000535:S2050509420000535_inline3.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20201119143046923-0262:S2050509420000535:S2050509420000535_inline4.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20201119143046923-0262:S2050509420000535:S2050509420000535_inline5.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20201119143046923-0262:S2050509420000535:S2050509420000535_inline6.png?pub-status=live)
- 6
- Cited by