Some properties of N-supercyclic operators

• Autorzy: P. S. Bourdon , N. S. Feldman , J. H. Shapiro
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A16: Cyclic vectors, hypercyclic and chaotic operators
• 15A99: Miscellaneous topics
• 47B20: Subnormal operators, hyponormal operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 165
• Numer: 2
• Strony: 135-157

Daty

wydano

2004

Twórcy

autor

P. S. Bourdon

• Washington and Lee University, Lexington, VA 24450, U.S.A.

autor

N. S. Feldman

• Washington and Lee University, Lexington, VA 24450, U.S.A.

autor

J. H. Shapiro

• Michigan State University, East Lansing, MI 48824, U.S.A.

Identyfikatory

DOI

10.4064/sm165-2-4