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A zk-invariant subspace without the wandering property

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2019-04-15
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Elsevier
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Abstract
We study operators of multiplication by zk in Dirichlet-type spaces Dα. We establish the existence of k and α for which some zk-invariant subspaces of Dα 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 zk, for any k≥6.
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Dirichlet spaces, Wandering property, Invariant subspaces, Multiplication operators, Shift operator, Bergman spaces
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Seco, D. (2019). A z-invariant subspace without the wandering property. Journal of Mathematical Analysis and Applications, 472(2), pp. 1377–1400.