On hypercyclicity and supercyclicity criteria

Dedicated to Professor Joel Shapiro on the occasion of his sixtieth birthday. Abstract. We show that the Hypercyclicity Criterion coincides with other existing hypercyclicity criteria and prove that a wide class of hypercyclic op-erators satisfy the Criterion. The results obtained extend or improve earlier work of several authors. We also unify the different versions of the Supercyclic-ity Criterion and show that operators with dense generalized kernel and dense range are supercyclic