Jordan Triple Morphisms and Maps Preserving Ternary Function Calculus on $$\boldsymbol{JB^{\ast}}$$-Triples

In the paper, triple continuous function calculus is investigated in connection with Jordan morphisms of Jordan triples. The main result shows that a linear map between two $$JB^{\ast}$$ -triples is a triple homomorphism if and only if it preserves triple function calculus induced just by one odd function (for example it is enough to consider the function $$\sin$$ ). Basic connections with the triple calculus on $$C^{\ast}$$ -algebras and Gelfand theory of $$JB^{\ast}$$ -triples is elucidated.

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