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Multiples of hypercyclic operators

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 27 Oct 2008 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 137, pages 1,397-1,403 (issn: 0002-9939, eissn: 1088-6826, Copyright policy )
Authors: Badea, Catalin; Grivaux, Sophie; Müller, Vladimir;

doi: 10.1090/s0002-9939-08-09696-2

handle: 11104/0171365

Multiples of hypercyclic operators

Abstract

We give a negative answer to a question of Prăjitură by showing that there exists an invertible bilateral weighted shift T T on ℓ 2 ( Z ) \ell _2(\mathbb {Z}) such that T T and 3 T 3T are hypercyclic but 2 T 2T is not. Moreover, any G δ G_\delta set M ⊆ ( 0 , ∞ ) M \subseteq (0,\infty ) which is bounded and bounded away from zero can be realized as M = { t > 0 ∣ t T  is hypercyclic } M=\{t>0 \mid tT \textrm { is hypercyclic}\} for some invertible operator T T acting on a Hilbert space.

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Keywords

[MATH] Mathematics [math], bilateral weighted shifts, hypercyclic operators

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
9
Average
Average
Average
hybrid
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