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arXiv · 2501.01272

Continuous Selection of Unitaries in II$_1$ Factors

Ilijas Farah·Andrea Vaccaro
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Abstract

We prove continuous-valued analogues of the basic fact that Murray-von Neumann subequivalence of projections in II$_1$ factors is completely determined by tracial evaluations. We moreover use this result to solve the so-called trace problem in the case of factorial trivial $W^\ast$-bundles whose base space has covering dimension at most 1. Our arguments are based on applications of a continuous selection theorem due to Michael to von Neumann algebras.

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Ilijas Farah, Andrea Vaccaro. 2025-01-02. Continuous Selection of Unitaries in II$_1$ Factors. https://arxiv.org/abs/2501.01272

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