Some Properties of N-Supercyclic
Operators
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| 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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