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Diameter two properties and polyhedrality

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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 study the (possible) relation between diameter two properties and various notions of polyhedrality. I-polyhedral spaces (being non-reflexive, M-embedded) have the strong diameter two property; however it turns out that even in II-polyhedral spaces the unit ball may contain slices of small diameter.

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Acknowledgements

The authors want to thank an anonymous referee for suggestions that improved the exposition.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Ginés López-Pérez & Abraham Rueda Zoca

  2. Instituto de Matemáticas de la Universidad de Granada (IEMath-GR), Granada, Spain

    Ginés López-Pérez

Authors
  1. Ginés López-Pérez
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  2. Abraham Rueda Zoca
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Corresponding author

Correspondence to Abraham Rueda Zoca.

Additional information

The research of G. López-Pérez was partially supported by MINECO (Spain) Grant MTM2015-65020-P and Junta de Andalucía Grant FQM-185.

The research of A. Rueda Zoca was supported by a research fellowship MECD (Spain) FPU2016/00015, by MINECO (Spain) Grant MTM2015-65020-P and by Junta de Andalucía Grants FQM-0185.

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López-Pérez, G., Rueda Zoca, A. Diameter two properties and polyhedrality. RACSAM 113, 131–135 (2019). https://doi.org/10.1007/s13398-017-0458-8

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  • DOI: https://doi.org/10.1007/s13398-017-0458-8

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