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 $$C_0^{\mathbb {T}}(L),$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">C0T(L), satisfies the complex Mazur–Ulam property, is, surjective isometry from unit sphere {T}}(L)$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">C0T(L) onto any Banach admits an extension to real linear between spaces.