no code implementations • 14 Jan 2021 • Thomas Jahn, Christian Richter
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.
Metric Geometry Functional Analysis
no code implementations • 26 May 2023 • Paul Geuchen, Thomas Jahn, Hannes Matt
We show that a width of $2n+2m+5$ is always sufficient and that in general a width of $\max\{2n, 2m\}$ is necessary.
