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Continuity properties of sequentially asymptotically center-complete spaces

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

We obtain formulae to calculate the asymptotic center and radius of bounded sequences in \({\mathcal {C}}_0(L)\) spaces. We also study the existence of continuous selectors for the asymptotic center map in general Banach spaces. In Hilbert spaces, even a Hölder-type estimation is given.

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Acknowledgments

The authors would like to thank Bernardo Cascales for his many suggestions that have greatly improved this paper. Our gratitude is also due to the referees for several helpful remarks. Finally, the second and third author would like to thank Carlos Angosto and Bernardo Cascales for their warm hospitality during a short stay at University of Murcia.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Paseo de Alfonso XIII 52, 30203, Cartagena, Murcia, Spain

    C. Angosto

  2. Departamento de Matemáticas, Universidad de Cádiz, Apdo. 40, 11510, Puerto Real, Cádiz, Spain

    M. C. Listán-García & F. Rambla-Barreno

Authors
  1. C. Angosto
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  2. M. C. Listán-García
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  3. F. Rambla-Barreno
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Corresponding author

Correspondence to F. Rambla-Barreno.

Additional information

C. Angosto was partially supported by the MINECO/FEDER project MTM2014-57838-C2-1-P. M. C. Listán-García and F. Rambla-Barreno authors were partially supported by Junta de Andalucía and FEDER Grant FQM-257.

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Angosto, C., Listán-García, M.C. & Rambla-Barreno, F. Continuity properties of sequentially asymptotically center-complete spaces. RACSAM 110, 809–822 (2016). https://doi.org/10.1007/s13398-015-0268-9

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  • DOI: https://doi.org/10.1007/s13398-015-0268-9

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