Convex sets and nearest points

Convex sets and nearest points
HTML articles powered by AMS MathViewer

by R. R. Phelps

Proc. Amer. Math. Soc. 8 (1957), 790-797

DOI: https://doi.org/10.1090/S0002-9939-1957-0087897-7

PDF | Request permission

References

Théorie des opérations linéaires

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
Herbert Busemann, Note on a theorem on convex sets, Mat. Tidsskr. B 1947 (1947), 32–34. MR 23087
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
Robert C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc. 61 (1947), 265–292. MR 21241, DOI 10.1090/S0002-9947-1947-0021241-4
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
Børge Jessen, Two theorems on convex point sets, Mat. Tidsskr. B 1940 (1940), 66–70 (Danish). MR 3721
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
V. L. Klee Jr., A characterization of convex sets, Amer. Math. Monthly 56 (1949), 247–249. MR 29519, DOI 10.2307/2304766

Sur quelques propriétés caractéristiques des ensembles convexes

Sur quelques propriétés caractéristiques des ensembles bornés non convexes