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Some properties of N-supercyclic operators

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Bourdon P., Feldman N., Shapiro J.

Studia Mathematica

2004

tom 165

nr 2

135-157

Let T be a continuous linear operator on a Hausdorff topological vector space 𝓧 over the field ℂ. We show that if T is N-supercyclic, i.e., if 𝓧 has an N-dimensional subspace whose orbit under T is dense in 𝓧, then T* has at most N eigenvalues (counting geometric multiplicity). We then show that N-supercyclicity cannot occur nontrivially in the finite-dimensional setting: the orbit of an N-dimensional subspace cannot be 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.

Ograniczanie wyników

1 Studia Mathematica

1 Bourdon P.

1 Feldman N.

1 Shapiro J.

1 2004

Wyniki wyszukiwania

Some properties of N-supercyclic operators