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On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces

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We survey mainly recent results on the two most important orthogonality types in normed linear spaces, namely on Birkhoff orthogonality and on isosceles (or James) orthogonality. We lay special emphasis on their fundamental properties, on their differences and connections, and on geometric results and problems inspired by the respective theoretical framework. At the beginning we also present other interesting types of orthogonality. This survey can also be taken as an update of existing related representations.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Extremadura, 06006, Badajoz, Spain

    Javier Alonso

  2. Fakultät für Mathematik, Technische Universität Chemnitz, 09107, Chemnitz, Germany

    Horst Martini

  3. Department of Applied Mathematics, Harbin University of Science and Technology, 150080, Harbin, China

    Senlin Wu

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  1. Javier Alonso
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  2. Horst Martini
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  3. Senlin Wu
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Correspondence to Senlin Wu.

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J. Alonso’s research was supported by MICINN (Spain) and FEDER (UE) grant MTM2008-05460, and by Junta de Extremadura grant GR10060 (partially financed with FEDER). Senlin Wu’s research was supported by National Natural Science Foundation of China (grant number 11001068), a foundation from the Ministry of Education of Heilongjiang Province (grant number 11541069), a foundation from Harbin University of Science and Technology (grant number 2009YF028), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, and by Deutsche Forschungsgemeinschaft.

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Alonso, J., Martini, H. & Wu, S. On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces. Aequat. Math. 83, 153–189 (2012). https://doi.org/10.1007/s00010-011-0092-z

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