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Spectrum of a weakly hypercyclic operator meets the unit circle

S. J. Dilworth·Vladimir G. Troitsky
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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.

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S. J. Dilworth, Vladimir G. Troitsky. 2002-08-24. Spectrum of a weakly hypercyclic operator meets the unit circle. https://arxiv.org/abs/math/0208193

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