A characterisation of inner product spaces by the maximal circumradius of spheres
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- 作者：Sebastian Scholtes (1) <br>
- 关键词：Primary 46C15 ; Secondary 46B20 ; Characterisation of inner product spaces ; Circumradius ; Euclidean four point property ; Parallelogram law
- 刊名：Archiv der Mathematik
- 出版年：2013
- 出版时间：September 2013
- 年：2013
- 卷：101
- 期：3
- 页码：235-241
- 全文大小：161KB
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- 作者单位：Sebastian Scholtes (1) <br><br>1. Institut f眉r Mathematik, RWTH Aachen University, Templergraben 55, 52062, Aachen, Germany <br>
- ISSN：1420-8938
文摘
We give a new characterisation of inner product spaces amongst normed vector spaces in terms of the maximal circumradius of spheres. It turns out that a normed vector space 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 the radius of the sphere.