The structure of triple homomorphisms onto prime algebras

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Abstract

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.

Original languageEnglish
JournalMathematical Proceedings of the Cambridge Philosophical Society
DOIs
Publication statusAccepted/In press - 2018 Jan 1

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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