Universal composition operators

A Hilbert space operator U is called \textit{universal} (in the sense of Rota) if every similar to a multiple restricted one its invariant subspaces. It follows that \textit{invariant subspace problem} for spaces equivalent statement all minimal subspaces are dimensional. In this article we characterize linear fractional composition operators Cϕf=f∘ϕ have universal translates on both classical Hardy H2(C+) and H2(D) half-plane unit disk, respectively. The new example here with affine symbol ϕa(z)=az+(1−a) $0