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Invariant subspaces for translation, dilation and multiplication semigroups

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Gallardo Gutiérrez, Eva A. and Partington, Jonathan R. (2009) Invariant subspaces for translation, dilation and multiplication semigroups. Journal d'analyse mathématique, 107 (1). pp. 65-78. ISSN 0021-7670

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Official URL: http://link.springer.com/content/pdf/10.1007%2Fs11854-009-0003-6.pdf


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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.


Item Type:Article
Uncontrolled Keywords:Composition operators
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:21043
Deposited On:24 Apr 2013 10:51
Last Modified:10 Aug 2018 08:52

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