Some Properties of
N-Supercyclic Operators
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Paul S. Bourdon, Nathan S. Feldman,
and Joel H. Shapiro
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Studia Mathematica
165 (2) (2004) 135--137
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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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