Subspace hypercyclicity

By Blair F. Madore, Rub'en A. Mart'inez Avendano. 2010

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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 subspacehypercyclicity 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/04fa24f25084df5e6f0b8adaa6c42bdd00448d01