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arXiv · 2402.00682

Generalised triple homomorphisms and Derivations

Jorge J. Garcés·Antonio M. Peralta
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Abstract

We introduce generalised triple homomorphism between Jordan Banach triple systems as a concept which extends the notion of generalised homomorphism between Banach algebras given by Jarosz and Johnson in 1985 and 1987, respectively. We prove that every generalised triple homomorphism between JB$^*$-triples is automatically continuous. When particularised to C$^*$-algebras, we rediscover one of the main theorems established by Johnson. We shall also consider generalised triple derivations from a Jordan Banach triple $E$ into a Jordan Banach triple $E$-module, proving that every generalised triple derivation from a JB$^*$-triple $E$ into $E^*$ is automatically continuous.

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Jorge J. Garcés, Antonio M. Peralta. 2024-02-01. Generalised triple homomorphisms and Derivations. https://doi.org/10.4153/cjm-2012-043-7

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