Every commutative JB^*-triple satisfies the complex Mazur–Ulam property

Abstract

We prove that every commutative JB^*-triple, represented as a space of continuous functions C_0^{mathbb {T}}(L), satisfies the complex Mazur–Ulam property, that is, every surjective isometry from the unit sphere of C_0^{mathbb {T}}(L) onto the unit sphere of any complex Banach space admits an extension to a surjective real linear isometry between the spaces.