N-supercyclic operators

Abstract

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 aren circles centered at the origin such that every component of the spectrum must intersect one of these circles.