Spectrum of a weakly hypercyclic operator meets the unit circle

S. J. Dilworth, Vladimir G. Troitsky

备注：: 3 pages, to appear in Proceedings of the Conference "Trends in Banach Spaces and Operator Theory", Memphis, 2001

英文摘要：

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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