Voiculescu's Theorem in Properly Infinite Factors
Operator Algebras
2025-08-04 v2
Abstract
In this paper, we investigate Voiculescu's theorem on approximate unitary equivalence in separable properly infinite factors. As applications, we establish the norm-denseness of the set of all reducible operators, prove a generalized Voiculescu's bicommutant theorem and a version of asymptotic bicommutant theorem, and obtain an interesting cohomological result. Additionally, we extend these results to multiplier algebras within separable type factors. At last, a concept of the nuclear length is introduced.
Keywords
Cite
@article{arxiv.2403.05799,
title = {Voiculescu's Theorem in Properly Infinite Factors},
author = {Donald Hadwin and Minghui Ma and Junhao Shen},
journal= {arXiv preprint arXiv:2403.05799},
year = {2025}
}