- April 2019
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- We study operators of multiplication by zk in Dirichlet-type spaces Dalfa. We establish the existence of k and alfa for which some zk-invariant subspaces of Dalfa 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.
- dirichlet spaces; wandering property; invariant subspaces; multiplication operators; shift operator; bergman spaces