[Cyclicité de certains opérateurs bicycliques]
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
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
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Evgeny Abakumov 1 ; Aharon Atzmon 2 ; Sophie Grivaux 3
@article{CRMATH_2007__344_7_447_0, author = {Evgeny Abakumov and Aharon Atzmon and Sophie Grivaux}, 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}, }
Evgeny Abakumov; Aharon Atzmon; Sophie Grivaux. Cyclicity of bicyclic operators. Comptes Rendus. Mathématique, Volume 344 (2007) no. 7, pp. 447-452. doi : 10.1016/j.crma.2007.02.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.02.008/
[1] Operators which are annihilated by analytic functions and invariant subspaces, Acta Math., Volume 144 (1980), pp. 27-63
[2] Generating sets for Beurling algebras, J. Approx. Theory, Volume 140 (2006), pp. 61-70
[3] Subnormal operators, Duke Math. J., Volume 22 (1955), pp. 75-94
[4] Completeness in
[5] Universal families and hypercyclic operators, Bull. Amer. Math. Soc., Volume 36 (1999), pp. 345-381
[6] Hyperinvariant subspaces of bilateral weighted shifts, Indiana Univ. Math. J., Volume 23 (1973/74), pp. 771-790
[7] Eigenvectors and cyclic vectors for bilateral weighted shifts, Rev. Un. Mat. Argentina, Volume 26 (1972/73), pp. 24-41
[8] Selected problems of weighted approximation and spectral analysis, Proc. Steklov Inst. Math., Volume 120 (1974) (English translation: Amer. Math. Soc., Providence, RI, 1976)
[9] Weighted shift operators and analytic function theory, Topics in Operator Theory, Math. Surveys, vol. 13, Amer. Math. Soc., Providence, RI, 1974, pp. 49-128
[10] Summability of the logarithm of a quasianalytic function, Dokl. Akad. Nauk SSSR, Volume 265 (1982), pp. 1297-1302 (English translation: Soviet Math. Dokl., 26, 1982, pp. 238-243)
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