Nous étudions la cyclicité de certains opérateurs bicycliques agissant sur des espaces de Banach séparables. Nos résultats s'appliquent en particulier aux opérateurs de décalage sur les espaces de suites pondérés . Nous prouvons également des résultats concernant la complétude des translatés d'une fonction dans certains espaces de Banach de fonctions sur .
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 . We also prove completeness results of translates in certain Banach spaces of functions on .
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@article{CRMATH_2007__344_7_447_0, author = {Abakumov, Evgeny and Atzmon, Aharon and Grivaux, Sophie}, title = {Cyclicity of bicyclic operators}, journal = {Comptes Rendus. Math\'ematique}, pages = {447--452}, publisher = {Elsevier}, volume = {344}, number = {7}, year = {2007}, doi = {10.1016/j.crma.2007.02.008}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.02.008/} }
TY - JOUR AU - Abakumov, Evgeny AU - Atzmon, Aharon AU - Grivaux, Sophie TI - Cyclicity of bicyclic operators JO - Comptes Rendus. Mathématique PY - 2007 SP - 447 EP - 452 VL - 344 IS - 7 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.02.008/ DO - 10.1016/j.crma.2007.02.008 LA - en ID - CRMATH_2007__344_7_447_0 ER -
%0 Journal Article %A Abakumov, Evgeny %A Atzmon, Aharon %A Grivaux, Sophie %T Cyclicity of bicyclic operators %J Comptes Rendus. Mathématique %D 2007 %P 447-452 %V 344 %N 7 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.02.008/ %R 10.1016/j.crma.2007.02.008 %G en %F CRMATH_2007__344_7_447_0
Abakumov, Evgeny; Atzmon, Aharon; Grivaux, Sophie. Cyclicity of bicyclic operators. Comptes Rendus. Mathématique, Tome 344 (2007) no. 7, pp. 447-452. doi : 10.1016/j.crma.2007.02.008. http://archive.numdam.org/articles/10.1016/j.crma.2007.02.008/
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