Linear orthogonality preservers between function spaces associated with commutative JB*-triples

Abstract

It is known, by Gelfand theory, that every commutative JB*-triple admits a representation as a space of continuous functions of the form

C-0(T) (L) = {alpha epsilon C-0(L) : alpha(lambda t) =lambda alpha(t), A lambda epsilon T, t epsilon L},

where L is a principal T-bundle and T denotes the unit circle in C. We provide a full technical description of all orthogonality preserving (non-necessarily continuous nor bijective) linear maps between commutative JB*-triples. Among the consequences of this representation, we obtain that every linear bijection preserving orthogonality between commutative JB*-triples is automatically continuous and bi-orthogonality preserving.