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arXiv · 1807.04679

A $Z^k$-invariant subspace without the wandering property

Daniel Seco
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Abstract

We study operators of multiplication by $z^k$ in Dirichlet-type spaces $D_\alpha$. We establish the existence of $k$ and $\alpha$ for which some $z^k$-invariant subspaces of $D_\alpha$ do not satisfy the wandering property. As a consequence of the proof, any Dirichlet-type space accepts an equivalent norm under which the wandering property fails for some space for the operator of multiplication by $z^k$, for any $k \geq 6$.

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Daniel Seco. 2018-07-12. A $Z^k$-invariant subspace without the wandering property. https://arxiv.org/abs/1807.04679

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