The structure of triple homomorphisms onto prime algebras

Research output: Contribution to journalArticle

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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Homomorphisms
Banach algebra
Algebra
C*-algebra
Standard Operator Algebra
JB*-triple
Associative Algebra
Semisimple
Idempotent
Homomorphism
Hilbert space
Arbitrary

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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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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