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Subspace hypercyclicity
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.Comment: 15 page
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