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arXiv · 2406.07774

Beurling and Model subspaces invariant under a universal operator

Ben Hur Eidt·S. Waleed Noor
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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 $C_{ϕ_a}f=f\circϕ_a$, where $ϕ_a(z) = az + 1 - a$ 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 Cesàro operator.

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Ben Hur Eidt, S. Waleed Noor. 2024-06-14. Beurling and Model subspaces invariant under a universal operator. https://arxiv.org/abs/2406.07774

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