Abstract
We prove a criterion that guarantees that in a given class of operators the set of hypercyclic ones is residual. We also prove the existence of quasinilpotent Volterra composition operators, \({V_\varphi}\) , such that both \({V_\varphi}\) and \({V_\varphi^\star}\) are supercyclic and both \({I + V_\varphi}\) and \({I + V_\varphi^\star}\) are hypercyclic.
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