On cleanness of von Neumann algebras
Operator Algebras
2022-01-13 v3 Rings and Algebras
Abstract
A unital ring is called clean (resp. strongly clean) if every element can be written as the sum of an invertible element and an idempotent (resp. an invertible element and an idempotent that commutes). T.Y. Lam proposed a question: which von Neumann algebras are clean as rings? In this paper, we characterize strongly clean von Neumann algebras and prove that all finite von Neumann algebras and all separable infinite factors are clean.
Keywords
Cite
@article{arxiv.2104.04350,
title = {On cleanness of von Neumann algebras},
author = {Lu Cui and Linzhe Huang and Wenming Wu and Wei Yuan and Hanbin Zhang},
journal= {arXiv preprint arXiv:2104.04350},
year = {2022}
}
Comments
19 pages(A citation mistake is corrected)