Coproximinality of linear subspaces in generalized Minkowski spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:504

Article

Jahn, Thomas¹  Richter, Christian² 

[1] Tech Univ Chemnitz, Fac Math, D-09107 Chemnitz, Germany

[2] Friedrich Schiller Univ, Inst Math, D-07737 Jena, Germany

关键词: Best coapproximation;    Coproximinal;    Gauge;    Hilbert space;    Minkowski space;    Norm;   

DOI  :  10.1016/j.jmaa.2021.125351

来源: Elsevier

【 摘 要 】

We show that, for vector spaces in which distance measurement is performed using a gauge, the existence of best coapproximations in 1-co dimensional closed linear subspaces implies in dimensions > 2 that the gauge is a norm, and in dimensions > 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. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free