Abstract
We study invariant subspaces in the context of the work of Katavolos and Power [9] and [10] when one of the semigroups considered is replaced by a discrete one. As a consequence, a rather striking connection is given with the study of the lattice of invariant subspaces of composition operators induced by automorphisms of the unit disc acting on the classical Hardy space. As a particular instance, our study concerns the lattice of invariant subspaces of those composition operators induced by hyperbolic automorphisms, and therefore with the Invariant Subspace Problem.
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Partially supported by Plan Nacional I+D grant no. MTM2006-06431 and Gobierno de Aragón research group Análisis Matemático y Aplicaciones, ref. DGA E-64.
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Gallardo-Gutiérrez, E.A., Partington, J.R. Invariant subspaces for translation, dilation and multiplication semigroups. J Anal Math 107, 65–78 (2009). https://doi.org/10.1007/s11854-009-0003-6
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DOI: https://doi.org/10.1007/s11854-009-0003-6