Suppose that is a separable normed space and the operators and are bounded on . In this paper, it is shown that if $AQ=QA$, is an isometry, and is a nilpotent then the operator is neither supercyclic nor weakly hypercyclic. Moreover, if the underlying space is a Hilbert space and is a co-isometric operator, then we give sufficient conditions under which the operator satisfies the supercyclicity criterion.
S. Yarmahmoodi. K. Hedayatian. B. Yousefi. "Supercyclicity and Hypercyclicity of an Isometry Plus a Nilpotent." Abstr. Appl. Anal. 2011 1 - 11, 2011. https://doi.org/10.1155/2011/686832