On criteria of Kasahara and Blumenthal for inner-product spaces
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- by Mahlon M. Day
- Proc. Amer. Math. Soc. 10 (1959), 92-100
- DOI: https://doi.org/10.1090/S0002-9939-1959-0106407-0
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References
- Leonard M. Blumenthal, Theory and applications of distance geometry, Oxford, at the Clarendon Press, 1953. MR 0054981
- Leonard M. Blumenthal, An extension of a theorem of Jordan and von Neumann, Pacific J. Math. 5 (1955), 161–167. MR 70155
- 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 normed linear spaces, Ann. of Math. vol. 36 (1935) pp. 705-718.
- S. Kakutani, Some characterizations of Euclidean space, Jpn. J. Math. 16 (1939), 93–97. MR 895, DOI 10.4099/jjm1924.16.0_{9}3
- Shouro Kasahara, A characterization of Hilbert space, Proc. Japan Acad. 30 (1954), 846–848. MR 69399
- I. J. Schoenberg, A remark on M. M. Day’s characterization of inner-product spaces and a conjecture of L. M. Blumenthal, Proc. Amer. Math. Soc. 3 (1952), 961–964. MR 52035, DOI 10.1090/S0002-9939-1952-0052035-9
- W. A. Wilson, A Relation Between Metric and Euclidean Spaces, Amer. J. Math. 54 (1932), no. 3, 505–517. MR 1506915, DOI 10.2307/2370894
Bibliographic Information
- © Copyright 1959 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 10 (1959), 92-100
- MSC: Primary 46.00; Secondary 52.00
- DOI: https://doi.org/10.1090/S0002-9939-1959-0106407-0
- MathSciNet review: 0106407