Supercyclicity and Hypercyclicity of an Isometry Plus a Nilpotent

الملخص EN

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.