Cyclicity of bicyclic operators

Evgeny Abakumov; Aharon Atzmon; Sophie Grivaux

doi:10.1016/j.crma.2007.02.008

Cyclicity of bicyclic operators

Evgeny Abakumov^*, Aharon Atzmon, Sophie Grivaux

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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Abstract

We study cyclicity of injective operators on separable Banach spaces which admit a bicyclic vector such that the norms of its images under the iterates of the operator satisfy certain growth conditions. Our results apply in particular to the shift operator acting on the weighted spaces of sequences ℓ_ω² (Z). We also prove completeness results of translates in certain Banach spaces of functions on R. To cite this article: E. Abakumov et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

Original language	English
Pages (from-to)	447-452
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	344
Issue number	7
DOIs	https://doi.org/10.1016/j.crma.2007.02.008
State	Published - 1 Apr 2007

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AU - Atzmon, Aharon

AU - Grivaux, Sophie

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AB - We study cyclicity of injective operators on separable Banach spaces which admit a bicyclic vector such that the norms of its images under the iterates of the operator satisfy certain growth conditions. Our results apply in particular to the shift operator acting on the weighted spaces of sequences ℓω2 (Z). We also prove completeness results of translates in certain Banach spaces of functions on R. To cite this article: E. Abakumov et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

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Cyclicity of bicyclic operators

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