Jordan triple product homomorphisms on Hermitian matrices to and from dimension one

Abstract

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 or the set of all nonnegative real numbers to the set of all Hermitian $n\times n$ complex matrices.

10 pages

Cited by in corpus (1)

• Jordan triple product homomorphisms on Hermitian matrices of dimension two