Linear bijections on von Neumann factors commuting with λ-Aluthge transform


We prove that a bijective linear transformation between von Neumann factors that commute with a λ-Aluthge transform is necessarily a non-zero scalar multiple of an algebra ∗-isomorphism in the case of algebras that are not of type I2. As for type I2 factors, that is, in the particular case of the algebra of 2 by 2 complex matrices, we also present a complete description of those transformations which is a bit different. Namely, non-zero scalar multiples of the sum of an algebra ∗-antiisomorphism and the negative of the trace functional times the identity also show up.

Publication Title

Bulletin of the London Mathematical Society