Spectrum of a weakly hypercyclic operator meets the unit circle
arXiv:math/0208193
Abstract
It is shown that every component of the spectrum of a weakly hypercyclic operator meets the unit circle. The proof is based on the lemma that a sequence of vectors in a Banach space whose norms grow at geometrical rate doesn't have zero in its weak closure.
3 pages, to appear in Proceedings of the Conference "Trends in Banach Spaces and Operator Theory", Memphis, 2001