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An Example of a Banach Space with Non-Lipschitzian Metric Projection on Any Straight Line

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Abstract

We construct an example of a three-dimensional strictly convex normed space on which the operator of metric projection onto any straight line does not satisfy the Lipschitz condition.

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Acknowledgments

The author wishes to express gratitude to P. A. Borodin for stating the problem and valuable remarks.

Funding

This work was supported by the Russian Foundation for Basic Research under grant 18-01-00333-a, by the program “Leading Scientific Schools” under grant NSh-6222.2018.1, and by the Foundation “BASIS” for Development of Theoretical Physics and Mathematics.

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Authors and Affiliations

  1. Moscow Center for Fundamental and Applied Mathematics, 119991, Moscow, Russia

    L. Sh. Burusheva

  2. Lomonosov Moscow State University, 119991, Moscow, Russia

    L. Sh. Burusheva

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  1. L. Sh. Burusheva
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Correspondence to L. Sh. Burusheva.

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Burusheva, L.S. An Example of a Banach Space with Non-Lipschitzian Metric Projection on Any Straight Line. Math Notes 109, 184–191 (2021). https://doi.org/10.1134/S0001434621010223

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  • DOI: https://doi.org/10.1134/S0001434621010223

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