| Let H be a complex Hilbert space, and let f(z)=(?)(BnZn),z∈Δ={z:|z|<1}, where {Bn} is a sequence of normal operators on H comm muting pairwise, such that ‖f(z)‖<1 for z∈Δ and 1∈σ(B1). If ?T∈X={A∈F(H): A commutes with every Bn and σ(A)?Δ} with f(T)=T, then T is the unique one in X satisfying the equation, and T must be normal. |
