Beurling and Model subspaces invariant under a universal operator

Abstract

In this article, we characterize the Beurling and Model subspaces of the Hardy-Hilbert space $H^2(\mathbb{D})$ invariant under the composition operator $C_{\ddot{I}{•}_a}f=f\circ \ddot{I}{•}_a$, where $\ddot{I}{•}_a(z)=az+1-a$ 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 Cesà ro operator.

9 pages, updated references