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 formC0T(L)={a∈C0(L):a(λt)=λa(t),∀λ∈T,t∈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.