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An integral characterization of Euclidean space

Published online by Cambridge University Press:  17 April 2009

J.M. Borwein
J.M. Borwein
Affiliation:
Department of Mathematics, Dalnousie University, Halifax, Nova Scotia, Canada B3H 4H8.
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Abstract

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We show that recent integral versions of the classic Jordan-Von Neumann characterization of Euclidean space may he viewed as special cases of a general averaging principle over sets of isometries.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 3 , June 1984 , pp. 357 - 364
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Busemann, H., The geometry of geodisics (Academic Press, New York, 1955).Google Scholar
[2]Day, M.M., Normed linear spaces, Third Edition (Springer-Verlag, Berlin, Heidelberg, New York, 1973).CrossRefGoogle Scholar
[3]Day, M.M., “Comments on notes of Stanojević et al”, Proc. Amer. Math. Soc. 81 (1981), 554–555.Google Scholar
[4]Penico, A.J. and Stanojević, Č.V., “An integral analogue to parallelogram law”, Proc. Amer. Math. Soc. 79 (1980), 427–430.CrossRefGoogle Scholar
[5]Rudin, W., Functional analysis (McGraw-Hill, New York, 1973).Google Scholar
[6]Stanojević, Č.V. and Suchanek, A.M., “Integral identities of norms and characterization of inner product spaces”, Proc. Amer. Math. Soc. 81 (1981), 101–103.CrossRefGoogle Scholar