### 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 language | English |
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Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

DOIs | |

Publication status | Accepted/In press - 2018 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

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**The structure of triple homomorphisms onto prime algebras.** / Liu, Cheng-Kai.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The structure of triple homomorphisms onto prime algebras

AU - Liu, Cheng-Kai

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85055587336&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055587336&partnerID=8YFLogxK

U2 - 10.1017/S0305004118000737

DO - 10.1017/S0305004118000737

M3 - Article

AN - SCOPUS:85055587336

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

ER -