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Some new properties of composition operators associated with lens maps

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Abstract

We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space H 2. The last ones are connected with Hardy-Orlicz and Bergman-Orlicz spaces \({H^\psi }\) and \({B^\psi }\), and provide a negative answer to the question of knowing if all composition operators which are weakly compact on a non-reflexive space are norm-compact.

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Authors and Affiliations

  1. U-Artois, Laboratoire de Mathématiques de Lens EA 2462 Fédération CNRS Nord-Pas-de-Calais FR 2956, Faculté des Sciences Jean Perrin, Univ Lille Nord de France, Rue Jean Souvraz, S.P. 18, F-62 300, Lens, France

    Pascal Lefèvre & Daniel Li

  2. USTL, Laboratoire Paul Painlevé U.M.R. CNRS 8524 Fédération CNRS Nord-Pas-de-Calais FR 2956, Univ Lille Nord de France, F-59 655, Villeneuve d’Ascq Cedex, France

    Hervé Queffélec

  3. Facultad de Matemáticas Departamento de Análisis Matemático & IMUS, Universidad de Sevilla, Apartado de Correos 1160, 41 080, Sevilla, Spain

    Luis Rodríguez-Piazza

Authors
  1. Pascal Lefèvre
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  2. Daniel Li
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  3. Hervé Queffélec
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  4. Luis Rodríguez-Piazza
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Correspondence to Pascal Lefèvre.

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Lefèvre, P., Li, D., Queffélec, H. et al. Some new properties of composition operators associated with lens maps. Isr. J. Math. 195, 801–824 (2013). https://doi.org/10.1007/s11856-012-0164-3

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  • DOI: https://doi.org/10.1007/s11856-012-0164-3

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