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A holomorphic characterization of compact sets in Banach spaces

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Abstract

An extension of Lempert’s result about non approximability by entire functions of analytic functions on some open subsets of ℓ∞ is obtained for Banach spaces having a bounding non relatively compact set.We also prove that subsets A that are bounding for analytic functions defined in any of its neighborhoodswhose boundary lies at positive distance from A are relatively compact.

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Author information

Authors and Affiliations

  1. Departamento de Matemática, Instituto de Matemática e Estatística Universidade de São Paulo, Caixa Postal 66281, 05315-970, São Paulo, Brazil

    Humberto Carrión & Mary Lilian Lourenço

  2. Departamento de AnálisisMatemático Facultad de Matemáticas, Universidad de Valencia, 46.100, Burjasot-Valencia, Spain

    Pablo Galindo

Authors
  1. Humberto Carrión
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  2. Pablo Galindo
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  3. Mary Lilian Lourenço
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Corresponding author

Correspondence to Mary Lilian Lourenço.

Additional information

Supported partially by FAPESP 2012/01015-9 andMTM 2014-53241-P (MINECO, Spain).

Supported partially by FAPESP 2012/01015-9.

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Carrión, H., Galindo, P. & Lourenço, M.L. A holomorphic characterization of compact sets in Banach spaces. Bull Braz Math Soc, New Series 47, 863–869 (2016). https://doi.org/10.1007/s00574-016-0193-3

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  • DOI: https://doi.org/10.1007/s00574-016-0193-3

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