Some Properties of
N-Supercyclic Operators


Paul S. Bourdon, Nathan S. Feldman, and Joel H. Shapiro


Studia Mathematica 165 (2) (2004) 135--137
Abstract: We call a continuous linear operator T on a Hausdorff topological vector space "N-supercyclic", there is an N dimensional subspace whose T-orbit is dense. We show that such an operator can have at most N eigenvalues, counting geometric multiplicity. We show further that N-supercyclicity cannot occur nontrivially in the finite dimensional setting: the orbit of an N dimensional subspace cannotbe dense in an N+1 dimensional space. Finally, we show that a subnormal operator on an infinite-dimensional Hilbert space can never be N-supercyclic.

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