## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- Workshop/Miniconference on Functional Analysis and Optimization. Simon Fitzpatrick and John Giles, eds. Proceedings of the Centre for Mathematical Analysis, v. 20. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1988), 16 - 23

### An approximation theoretic characterisation of inner product spaces

#### Abstract

Two approximation theoretic properties of Hilbert spaces used in the proof of a result concerning Chebyshev sets obtained by Frerking and Westphal [4] are discussed. Investigation of one leads to a characterisation of inner product spaces of dimension at least three; it is an improvement of one due to Berens [3]. The other property is shared by all finite dimensional spaces [3] and here a topological result of which that fact is a simple consequence is proved.

#### Article information

**Dates**

First available in Project Euclid:
18 November 2014

**Permanent link to this document**

https://projecteuclid.org/
euclid.pcma/1416340098

**Mathematical Reviews number (MathSciNet)**

MR1009589

#### Citation

Brown, A. L. An approximation theoretic characterisation of inner product spaces. Workshop/Miniconference on Functional Analysis and Optimization, 16--23, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1988. https://projecteuclid.org/euclid.pcma/1416340098