This is an announcement for the paper "A characterisation of inner product spaces by the maximal circumradius of spheres" by Sebastian Scholtes.
Abstract: We will give a new characterisation of inner product spaces amongst normed vector spaces in terms of the maximal cirumradius of spheres. It will turn out that a normed vector space $(X,\norm{\cdot})$ with $\dim X\geq 2$ is an inner product space if and only if all spheres are not degenerate, i.e. the maximal circumradius of points on the sphere equals their radius.
Archive classification: math.FA math.CA math.MG
Mathematics Subject Classification: 46C15, 46B20
Remarks: 8 pages
Submitted from: sebastian.scholtes@rwth-aachen.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.0503
or