Trichotomy for the orbits of a hypercyclic operator on a Banach space
Abstract
We obtain a trichotomy for the orbits of a hypercyclic operator T on a separable Banach space X: (1) every vector is mean asymptotic to zero; (2) generic vectors are absolutely mean irregular; (3) every hypercyclic vector is mean divergent to infinity. Examples of weighted backward shifts on p show that all three cases can happen.
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