We prove that every commutative JB$$^*$$
∗
-triple, represented as a space of continuous functions $$C_0^{\mathbb {T}}(L),$$
C
0
T
(
L
)
,
satisfies the complex Mazur–Ulam property, that is, every surjective isometry from the unit sphere of $$C_0^{\mathbb {T}}(L)$$
C
0
T
(
L
)
onto the unit sphere of any complex Banach space admits an extension to a surjective real linear isometry between the spaces.
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