Let U be an algebra with center Z(U). A mapping φ : U → U is centralizing if φ(a)a − aφ(a) ∈ Z(U) for all a ∈ U. We prove that any continuous centralizing linear map φ on a proper H∗-algebra U with U = 2(Γ, Uγ) ( each Uγ is a minimal closed ideal of U) is of the form φ(a) = ca + μ(a), a ∈ U, where c ∈ ∞(Γ) and μ : U → Z(U) is a continuous linear map. Then we examine the automatic continuity of centralizing linear maps on Banach algebras and by using it, a characterization of proper H∗-algebras based on the automatic continuity of centralizing linear maps is given
