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Jordan triple product homomorphisms on Hermitian matrices to and from dimension one (1506.07819v1)
Published 22 Jun 2015 in math.RA and math.OA
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.