Antisupercyclic Operators and Orbits of the Volterra Operator

摘要

We say that a bounded linear operator T acting on a Banach space B is antisupercyclic if for any x ∈ B either Tnx = 0 for some positive integer n or the sequence {Tnx/‖Tnx‖} weakly converges to zero in B. Antisupercyclicity of T means that the angle criterion of supercyclicity is not satisfied for T in the strongest possible way. Normal antisupercyclic operators and antisupercyclic bilateral weighted shifts are characterized.