Non-linear Jordan triple automorphisms of sets of self-adjoint matrices and operators
Volume 173 / 2006
Studia Mathematica 173 (2006), 39-48 MSC: Primary 47B49. DOI: 10.4064/sm173-1-3
We consider the so-called Jordan triple automorphisms of some important sets of self-adjoint operators without the assumption of linearity. These transformations are bijective maps which satisfy the equality $$ \phi(ABA)=\phi(A)\phi(B)\phi(A) $$ on their domains. We determine the general forms of these maps (under the assumption of continuity) on the sets of all invertible positive operators, of all positive operators, and of all invertible self-adjoint operators.