Some characterizations of inner-product spaces
HTML articles powered by AMS MathViewer
- by Mahlon M. Day
- Trans. Amer. Math. Soc. 62 (1947), 320-337
- DOI: https://doi.org/10.1090/S0002-9947-1947-0022312-9
- PDF | Request permission
References
- S. Banach, Théorie des opérations linéaires, Monografje Matematyczne, Warsaw, 1932.
- Garrett Birkhoff, Orthogonality in linear metric spaces, Duke Math. J. 1 (1935), no. 2, 169–172. MR 1545873, DOI 10.1215/S0012-7094-35-00115-6
- H. F. Bohnenblust and A. Sobczyk, Extensions of functionals on complex linear spaces, Bull. Amer. Math. Soc. 44 (1938), no. 2, 91–93. MR 1563688, DOI 10.1090/S0002-9904-1938-06691-8
- James A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), no. 3, 396–414. MR 1501880, DOI 10.1090/S0002-9947-1936-1501880-4
- Mahlon M. Day, Polygons circumscribed about closed convex curves, Trans. Amer. Math. Soc. 62 (1947), 315–319. MR 22686, DOI 10.1090/S0002-9947-1947-0022686-9
- Mahlon M. Day, Uniform convexity in factor and conjugate spaces, Ann. of Math. (2) 45 (1944), 375–385. MR 10779, DOI 10.2307/1969275
- Frederick A. Ficken, Note on the existence of scalar products in normed linear spaces, Ann. of Math. (2) 45 (1944), 362–366. MR 10255, DOI 10.2307/1969273
- Maurice Fréchet, Sur la définition axiomatique d’une classe d’espaces vectoriels distanciés applicables vectoriellement sur l’espace de Hilbert, Ann. of Math. (2) 36 (1935), no. 3, 705–718 (French). MR 1503246, DOI 10.2307/1968652
- R. C. James, Orthogonality in normed linear spaces, Duke Math. J. 12 (1945), 291–302. MR 12199
- Robert C. James, Inner product in normed linear spaces, Bull. Amer. Math. Soc. 53 (1947), 559–566. MR 21242, DOI 10.1090/S0002-9904-1947-08831-5
- 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
- S. Kakutani, Some characterizations of Euclidean space, Jpn. J. Math. 16 (1939), 93–97. MR 895, DOI 10.4099/jjm1924.16.0_{9}3
- R. S. Phillips, A characterization of Euclidean spaces, Bull. Amer. Math. Soc. 46 (1940), 930–933. MR 3444, DOI 10.1090/S0002-9904-1940-07336-7
Bibliographic Information
- © Copyright 1947 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 62 (1947), 320-337
- MSC: Primary 46.3X
- DOI: https://doi.org/10.1090/S0002-9947-1947-0022312-9
- MathSciNet review: 0022312