Continuous selection of unitaries in II₁ factors
Abstract
We prove continuous-valued analogues of the basic fact that Murray–von Neumann subequivalence of projections in II 1 _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 ∗ W^\ast -bundles whose base space has covering dimension at most 1. Our arguments are based on applications to von Neumann algebras of a continuous selection theorem due to Michael.
Fields of Study & Subjects
Advanced Operator Algebra Research
Advanced Banach Space Theory
Holomorphic and Operator Theory
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 4
- Pages
- 1609–1622
- Publication date
- 10 February 2026
- Language
- EN