Generalised triple homomorphisms and Derivations

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${}^{\ast }$-triples is automatically continuous. When particularised to C${}^{\ast }$-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${}^{\ast }$-triple $E$ into $E^{\ast }$ is automatically continuous.