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## $n$-supercyclic operators

### Tom 151 / 2002

Studia Mathematica 151 (2002), 141-159 MSC: 47A16, 47B20, 47B40. DOI: 10.4064/sm151-2-3

#### Streszczenie

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.

#### Autorzy

• Nathan S. FeldmanDepartment of Mathematics
Washington and Lee University
Lexington, VA 24450, U.S.A.
e-mail

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