Complete characterizations of left or right symmetric points for (strong) Birkhoff orthogonality in von Neumann algebras and abelian unital C⁎-algebras are given. As an application, we show that every linear strong Birkhoff orthogonality preserver between von Neumann algebras is an algebraic ⁎-isomorphism.
- (Strong) Birkhoff orthogonality
- Linear preserver
- Symmetric point
- von Neumann algebra