In this article, we characterize the Beurling and Model subspaces of the Hardy-Hilbert space $H^2(\mathbb{ D})$ invariant under the composition operator $C_{ \phi_a}f=f\circ\phi_a$, where $\phi_a(z) = az + 1 - a$ for $a \in (0,1)$ is an affine self-map of the open unit disk $\mathbb{ D}$. These operators have universal translates (in the sense of Rota) and have attracted attention recently due to their connection with the Invariant Subspace Problem (ISP) and the classical Ces\`aro operator.
Categories: math.FA