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Cyclicity of bicyclic operators

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(omega)(2) (Z). We also prove completeness results of translates in certain Banach spaces of functions
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Evgeny Abakumov, Aharon Atzmon, Sophie Grivaux. Cyclicity of bicyclic operators. Comptes Rendus Mathématique, Elsevier Masson, 2007, 344 (7), pp.447--452. ⟨10.1016/j.crma.2007.02.008⟩. ⟨hal-00693090⟩

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