Jordan triple product homomorphisms on Hermitian matrices to and from dimension one
Jordan triple product homomorphisms on Hermitian matrices to and from dimension one
We characterise all Jordan triple product homomorphisms, that is, mappings $\Phi$ satisfying $$ \Phi(ABA) = \Phi(A)\Phi(B)\Phi(A) $$ from the set of all Hermitian $n \times n$ complex matrices to the field of complex numbers. Further we characterise all Jordan triple product homomorphisms from the field of complex or real numbers …