Orthogonal unitary bases and a subfactor conjecture

Crann, Jason; Kribs, David; Pereira, Rajesh

doi:10.1090/proc/16346

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.

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