Subspace hypercyclicity |
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Authors: | Blair F Madore |
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Institution: | a Department of Mathematics, State University of New York College at Potsdam, Potsdam, NY 13676-2294, USA b Centro de Investigación en Matemáticas, Universidad Autónoma del Estado de Hidalgo, Ciudad Universitaria, Carr. Pachuca-Tulancingo, km 4.5, Pachuca, Hidalgo 42184, Mexico |
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Abstract: | A bounded linear operator T on Hilbert space is subspace-hypercyclic for a subspace M if there exists a vector whose orbit under T intersects the subspace in a relatively dense set. We construct examples to show that subspace-hypercyclicity is interesting, including a nontrivial subspace-hypercyclic operator that is not hypercyclic. There is a Kitai-like criterion that implies subspace-hypercyclicity and although the spectrum of a subspace-hypercyclic operator must intersect the unit circle, not every component of the spectrum will do so. We show that, like hypercyclicity, subspace-hypercyclicity is a strictly infinite-dimensional phenomenon. Additionally, compact or hyponormal operators can never be subspace-hypercyclic. |
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Keywords: | Hypercyclicity Dynamics of linear operators in Hilbert space |
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