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arXiv · 1001.5320

Subspace hypercyclicity

Blair Madore·Rubén A. Martínez Avendaño
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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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Blair Madore, Rubén A. Martínez Avendaño. 2010-01-29. Subspace hypercyclicity. https://doi.org/10.1016/j.jmaa.2010.07.049

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