A nonlinear characterization of type I factors among von Neumann algebras based on strong Birkhoff–James orthogonality is given. As an application, it is shown that if a von Neumann algebra is isomorphic to a type I factor with respect to the structure of strong Birkhoff–James orthogonality, then they are ∗ -isomorphic as von Neumann algebras.
- Nonlinear classification
- Strong Birkhoff–James orthogonality
- Type I factor
- von Neumann algebra