A remark on M. M. Day’s characterization of inner-product spaces and a conjecture of L. M. Blumenthal

Schoenberg, I. J.

doi:10.1090/S0002-9939-1952-0052035-9

Proceedings of the American Mathematical Society

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A remark on M. M. Day’s characterization of inner-product spaces and a conjecture of L. M. Blumenthal
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by I. J. Schoenberg

Proc. Amer. Math. Soc. 3 (1952), 961-964

DOI: https://doi.org/10.1090/S0002-9939-1952-0052035-9

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References

Mahlon M. Day, Some characterizations of inner-product spaces, Trans. Amer. Math. Soc. 62 (1947), 320–337. MR 22312, DOI 10.1090/S0002-9947-1947-0022312-9
P. Jordan and J. Von Neumann, On inner products in linear, metric spaces, Ann. of Math. (2) 36 (1935), no. 3, 719–723. MR 1503247, DOI 10.2307/1968653
I. J. Schoenberg, On metric arcs of vanishing Menger curvature, Ann. of Math. (2) 41 (1940), 715–726. MR 2903, DOI 10.2307/1968849