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arXiv · 1904.02974

On the wandering property in Dirichlet spaces

Eva Gallardo-Gutiérrez·Jonathan Partington·Daniel Seco
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Abstract

We show that in a scale of weighted Dirichlet spaces $D_{\alpha}$, including the Bergman space, given any finite Blaschke product $B$ there exists an equivalent norm in $D_{\alpha}$ such that $B$ satisfies the wandering subspace property with respect to such norm. This extends, in some sense, previous results by Carswell, Duren and Stessin. As a particular instance, when $B(z)=z^k$ and $|\alpha| \leq \frac{\log (2)}{\log(k+1)}$, the chosen norm is the usual one in $D_\alpha$.

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Eva Gallardo-Gutiérrez, Jonathan Partington, Daniel Seco. 2019-04-05. On the wandering property in Dirichlet spaces. https://arxiv.org/abs/1904.02974

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