Coproximinality of linear subspaces in generalized Minkowski spaces

[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.

[发布日期] 2021-12-01

[关键词] Best coapproximation;Coproximinal;Gauge;Hilbert space;Minkowski space;Norm