Orthogonal unitary bases and a subfactor conjecture
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- by Jason Crann, David W. Kribs and Rajesh Pereira
- Proc. Amer. Math. Soc. 151 (2023), 3793-3799
- DOI: https://doi.org/10.1090/proc/16346
- Published electronically: June 6, 2023
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Abstract:
We show that any finite dimensional von Neumann algebra admits an orthonormal unitary basis with respect to its standard trace. We also show that a finite dimensional von Neumann subalgebra of $M_n(\mathbb {C})$ admits an orthonormal unitary basis under normalized matrix trace if and only if the normalized matrix trace and standard trace of the von Neumann subalgebra coincide. As an application, we verify a recent conjecture of Bakshi-Gupta [Glasg. Math. J. 64 (2022), pp. 586–602], showing that any finite-index regular inclusion $N\subseteq M$ of $II_1$-factors admits an orthonormal unitary Pimsner-Popa basis.References
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Bibliographic Information
- Jason Crann
- Affiliation: School of Mathematics & Statistics, Carleton University, Ottawa, Ontario H1S 5B6, Canada
- MR Author ID: 908052
- Email: jasoncrann@cunet.carleton.ca
- David W. Kribs
- Affiliation: Department of Mathematics & Statistics, University of Guelph, Guelph, Ontario N1G 2W1, Canada
- MR Author ID: 653737
- Email: dkribs@uoguelph.ca
- Rajesh Pereira
- Affiliation: Department of Mathematics & Statistics, University of Guelph, Guelph, Ontario N1G 2W1, Canada
- MR Author ID: 720521
- ORCID: 0000-0002-3041-4672
- Email: pereirar@uoguelph.ca
- Received by editor(s): August 21, 2022
- Received by editor(s) in revised form: November 6, 2022
- Published electronically: June 6, 2023
- Additional Notes: The first author was partially supported by the NSERC Discovery Grant RGPIN-2017-06275. The second author was partially supported by the NSERC Discovery Grant RGPIN-2018-400160. The third author was partially supported by the NSERC Discovery Grant RGPIN-2022-04149.
- Communicated by: Adrian Ioana
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 3793-3799
- MSC (2020): Primary 46L37, 15B10, 81P45
- DOI: https://doi.org/10.1090/proc/16346
- MathSciNet review: 4607624