Triple homomorphisms on C∗-algebras and JB∗-triples have been studied in the literature. From the viewpoint of associative algebras, we characterise the structure of triple homomorphisms from an arbitrary †-algebra onto a prime ∗-algebra. As an application, we prove that every triple homomorphism from a Banach †-algebra onto a prime semisimple idempotent Banach ∗-algebra is continuous. The analogous results for prime C∗-algebras and standard operator ∗-algebras on Hilbert spaces are also described.
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Accepted/In press - 2018 Jan 1|
All Science Journal Classification (ASJC) codes