On Pimsner-Popa orthonormal basis and Popa's relative dimension of projections
Operator Algebras
2025-09-17 v2 Functional Analysis
Abstract
We show that any depth 2 subfactor with a simple first relative commutant has a unitary orthonormal basis. As a pleasant consequence, we produce new elements in the set of Popa's relative dimension of projections for such subfactors. We also construct infinitely many new elements in the set of relative dimension of projections for subfactors arising from complex Hadamard matrices and bi-unitary matrices.
Keywords
Cite
@article{arxiv.2311.13820,
title = {On Pimsner-Popa orthonormal basis and Popa's relative dimension of projections},
author = {Keshab Chandra Bakshi and Satyajit Guin},
journal= {arXiv preprint arXiv:2311.13820},
year = {2025}
}
Comments
Referee's suggestions incorporated, to appear in New York J. Math