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Almost square and octahedral norms in tensor products of Banach 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

The aim of this note is to study some geometrical properties like diameter two properties, octahedrality and almost squareness in the setting of (symmetric) tensor product spaces. In particular, we show that the injective tensor product of two octahedral Banach spaces is always octahedral, the injective tensor product of an almost square Banach space with any Banach space is almost square, and the injective symmetric tensor product of an octahedral Banach space is octahedral.

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Acknowledgments

The research of J. Langemets was supported by institutional research funding IUT20-57 of the Estonian Ministry of Education and Research. Third author was partially supported by Junta de Andalucía Grants FQM-0199.

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Authors and Affiliations

  1. Institute of Mathematics and Statistics, University of Tartu, J. Liivi 2, 50409, Tartu, Estonia

    Johann Langemets

  2. NTNU, Norwegian University of Science and Technology, Postboks 1517, 6025, Ålesund, Norway

    Vegard Lima

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

    Abraham Rueda Zoca

Authors
  1. Johann Langemets
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  2. Vegard Lima
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  3. Abraham Rueda Zoca
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Correspondence to Abraham Rueda Zoca.

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Langemets, J., Lima, V. & Rueda Zoca, A. Almost square and octahedral norms in tensor products of Banach spaces. RACSAM 111, 841–853 (2017). https://doi.org/10.1007/s13398-016-0324-0

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  • DOI: https://doi.org/10.1007/s13398-016-0324-0

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