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arXiv · 2101.05594

Coproximinality of linear subspaces in generalized Minkowski spaces

Thomas Jahn·Christian Richter
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Abstract

We show that, for vector spaces in which distance measurement is performed using a gauge, the existence of best coapproximations in $1$-codimensional closed linear subspaces implies in dimensions $\geq 2$ that the gauge is a norm, and in dimensions $\geq 3$ that the gauge is even a Hilbert space norm. We also show that coproximinality of all closed subspaces of a fixed dimension implies coproximinality of all subspaces of all lower finite dimensions.

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Thomas Jahn, Christian Richter. 2021-01-14. Coproximinality of linear subspaces in generalized Minkowski spaces. https://arxiv.org/abs/2101.05594

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