diff --git a/src/topology/continuous_function/bounded.lean b/src/topology/continuous_function/bounded.lean
index 5168d1e1448b2..f3c1040617bd2 100644
--- a/src/topology/continuous_function/bounded.lean
+++ b/src/topology/continuous_function/bounded.lean
@@ -834,6 +834,9 @@ instance : has_scalar 𝕜 (α →ᵇ β) :=
 @[simp] lemma coe_smul (c : 𝕜) (f : α →ᵇ β) : ⇑(c • f) = λ x, c • (f x) := rfl
 lemma smul_apply (c : 𝕜) (f : α →ᵇ β) (x : α) : (c • f) x = c • f x := rfl
 
+instance [has_scalar 𝕜ᵐᵒᵖ β] [is_central_scalar 𝕜 β] : is_central_scalar 𝕜 (α →ᵇ β) :=
+{ op_smul_eq_smul := λ _ _, ext $ λ _, op_smul_eq_smul _ _ }
+
 instance : has_bounded_smul 𝕜 (α →ᵇ β) :=
 { dist_smul_pair' := λ c f₁ f₂, begin
     rw dist_le (mul_nonneg dist_nonneg dist_nonneg),