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The structure of triple homomorphisms onto prime algebras

Published online by Cambridge University Press:  23 October 2018

CHENG–KAI LIU
CHENG–KAI LIU*
Affiliation:
Department of Mathematics, National Changhua University of Education, No. 1 Jinde Road, Changhua City, Changhua County 50007, Taiwan, R.O.C. e-mail: ckliu@cc.ncue.edu.tw
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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.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 2 , March 2020 , pp. 345 - 360
Copyright
Copyright © Cambridge Philosophical Society 2018 

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