Supercyclicity and hypercyclicity of an isometry plus a nilpotent (Q554935)

Summary: Suppose that \(X\) is a separable normed space and the operators \(A\) and \(Q\) are bounded on \(X\). In this paper, it is shown that, if \(AQ = QA\), \(A\) is an isometry, and \(Q\) is a nilpotent, then the operator \(A + Q\) is neither supercyclic nor weakly hypercyclic. Moreover, if the underlying space is a Hilbert space and \(A\) is a co-isometric operator, then we give sufficient conditions under which the operator \(A + Q\) satisfies the supercyclicity criterion.