关键词: Cyclic性, Supercyclic性, Hypercyclic性

Abstract: According to a Sufficient and necessary condition for a sequence of operators to be Hypercyclic, we obtained a criterion for an operator to be Supercyclic. Applying this criterion to the bilateral weighted shifts with nonzero weights, we gave a Sufficient and necessary condition for a bilateral weighted shift with nonzero weights to satisfy this criterion.

Key words: Cyclic, Supercyclic, Hypercyclic