Jordan Triple Product Homomorphisms on Triangular Matrices to and from Dimension One
Keyword(s):
A map $\Phi$ is a Jordan triple product (JTP for short) homomorphism whenever $\Phi(A B A)= \Phi(A) \Phi(B) \Phi(A)$ for all $A,B$. We study JTP homomorphisms on the set of upper triangular matrices $\mathcal{T}_n(\mathbb{F})$, where $\Ff$ is the field of real or complex numbers. We characterize JTP homomorphisms $\Phi: \mathcal{T}_n(\mathbb{C}) \to \mathbb{C}$ and JTP homomorphisms $\Phi: \mathbb{F} \to \mathcal{T}_n(\mathbb{F})$. In the latter case we consider continuous maps and the implications of omitting the assumption of continuity.
2015 ◽
Vol 64
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pp. 1669-1678
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