A nonlinear characterization of type I factors based on strong Birkhoff-James orthogonality

摘要

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.