Proceedings of the Centre for Mathematics and its Applications

An approximation theoretic characterisation of inner product spaces

A. L. Brown

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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

Source
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

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


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