A Z^k-invariant subspace without the wandering property

2018/07/12 by Seco, Daniel
#30H20 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47A15 #Secondary 30H10

paper · doi:10.48550/arxiv.1807.04679

Abstract

We study operators of multiplication by z^k in Dirichlet-type spaces D_α. We establish the existence of k and α for which some z^k-invariant subspaces of D_α 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 ≥ 6.

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