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An integral characterization of Euclidean space

  • J.M. Borwein (a1)
Abstract

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.

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References
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[1]Busemann, H., The geometry of geodisics (Academic Press, New York, 1955).
[2]Day, M.M., Normed linear spaces, Third Edition (Springer-Verlag, Berlin, Heidelberg, New York, 1973).
[3]Day, M.M., “Comments on notes of Stanojević et al”, Proc. Amer. Math. Soc. 81 (1981), 554555.
[4]Penico, A.J. and Stanojević, Č.V., “An integral analogue to parallelogram law”, Proc. Amer. Math. Soc. 79 (1980), 427430.
[5]Rudin, W., Functional analysis (McGraw-Hill, New York, 1973).
[6]Stanojević, Č.V. and Suchanek, A.M., “Integral identities of norms and characterization of inner product spaces”, Proc. Amer. Math. Soc. 81 (1981), 101103.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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