Spectrum of a weakly hypercyclic operator meets the unit circle

Details Spectrum of a weakly hypercyclic operator meets the unit circle Spectrum of a weakly hypercyclic operator meets the unit circle

2002-08-24

arxiv.org/abs/math/0208193v1

Mathematics

Functional Analysis

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

Scientific paper

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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