$n$-supercyclic operators

Nathan S. Feldman¹

¹ Department of Mathematics Washington and Lee University Lexington, VA 24450, U.S.A.

Studia Mathematica, Tome 151 (2002) no. 2, pp. 141-159

Résumé

We show that there are linear operators on Hilbert space that have $n$-dimensional subspaces with dense orbit, but no $(n-1)$-dimensional subspaces with dense orbit. This leads to a new class of operators, called the $n$-supercyclic operators. We show that many cohyponormal operators are $n$-supercyclic. Furthermore, we prove that for an $n$-supercyclic operator, there are $n$ circles centered at the origin such that every component of the spectrum must intersect one of these circles.

Détail

DOI : 10.4064/sm151-2-3

Keywords: there linear operators hilbert space have n dimensional subspaces dense orbit n dimensional subspaces dense orbit leads class operators called n supercyclic operators many cohyponormal operators n supercyclic furthermore prove n supercyclic operator there circles centered origin every component spectrum intersect these circles