ORBITS OF PARANORMAL OPERATORS

Masuo Itoh (Japan)

Received June 23, 2008

Abstract

In this paper, we show the following facts. If T is paranormal operator, then T is never supercyclic, is power regular, has a non-trivial hyperinvariant subspace and is not weakly hypercyclic, which generalizes a result due to Bourdon [2] and Sanders [4].

Keywords and phrases: hypercyclic, supercyclic, weakly hypercyclic, power regular, paranormal operator.