James, Robert C. Orthogonality and linear functionals in normed linear spaces. (English) Zbl 0037.08001 Trans. Am. Math. Soc. 61, 285-292 (1947). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 200 Documents Keywords:Functional analysis PDF BibTeX XML Cite \textit{R. C. James}, Trans. Am. Math. Soc. 61, 285--292 (1947; Zbl 0037.08001) Full Text: DOI OpenURL References: [1] Guido Ascoli, Sugli spazi lineari metrici e le loro varietà lineari, Ann. Mat. Pura Appl. 10 (1932), no. 1, 33 – 81 (Italian). · Zbl 0003.40902 [2] S. Banach, Théorie des opérations linéaires, Warsaw, 1932. · JFM 58.0420.01 [3] Garrett Birkhoff, Orthogonality in linear metric spaces, Duke Math. J. 1 (1935), no. 2, 169 – 172. · Zbl 0012.30604 [4] James A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), no. 3, 396 – 414. · Zbl 0015.35604 [5] Frederick A. Ficken, Note on the existence of scalar products in normed linear spaces, Ann. of Math. (2) 45 (1944), 362 – 366. · Zbl 0060.26203 [6] Robert Fortet, Remarques sur les espaces uniformément convexes, C. R. Acad. Sci. Paris 210 (1940), 497 – 499. · Zbl 0023.13004 [7] R. Fortet, Remarques sur les espaces uniformément convexes, Bull. Soc. Math. France 69 (1941), 23 – 46 (French). · Zbl 0026.32401 [8] M. Fréchet, Sur la notion de différentielle, J. Math. Pures Appl. vol. 16 (1937) pp. 233-250. · JFM 63.0193.04 [9] -, Sur la définition axiomatique d’une classe d’espaces vectoriels distanciés applicables vectoriellement sur l’espaces de Hilbert, Ann. of Math. vol. 36 (1935) pp. 705-718. · Zbl 0012.30701 [10] V. Gantmakher and V. Šmulian, Sur les espaces linéaires dont la sphere unitaire est faiblement compacte, C. R. (Doklady) Acad. Sci. URSS. vol. 17 (1937) pp. 91-94. · Zbl 0017.36003 [11] R. C. James, Orthogonality in normed linear spaces, Duke Math. J. 12 (1945), 291 – 302. · Zbl 0060.26202 [12] P. Jordan and J. Von Neumann, On inner products in linear, metric spaces, Ann. of Math. (2) 36 (1935), no. 3, 719 – 723. · JFM 61.0435.05 [13] H. Löwig, Komplexe Euklidische Räume von beliebiger endlicher oder transfiniter Dimensionzahl, Acta Litterarum Ac Scientiarum vol. 7 (1934-1935) pp. 1-33. · JFM 60.0324.01 [14] S. Mazur, Über convexe Mengen in linearen normierten Räumen, Studia Mathematica vol. 4 (1933) pp. 70-84. · JFM 59.1074.01 [15] -, Über schwache Konvergenz in den Räumen \( ({L^p})\), Studia Mathematica vol. 4 (1933) pp. 128-133. · JFM 59.1076.01 [16] D. Milman, On some criteria for the regularity of spaces of the type \( (B)\), C. R. (Doklady) Acad. Sci. URSS. vol. 20 (1938) pp. 243-246. · Zbl 0019.41601 [17] B. J. Pettis, A proof that every uniformly convex space is reflexive, Duke Math. J. 5 (1939), no. 2, 249 – 253. · Zbl 0021.32601 [18] B. D. Roberts, On the geometry of abstract vector spaces, Tôhoku Math. J. vol. 39 (1934) pp. 42-59. · Zbl 0009.16903 [19] V. Šmulian, On some geometrical properties of the unit sphere in the space of the type \( (B)\), Rec. Math. (Mat. Sbornik) N. S. vol. 48 (1938) pp. 90-94. · JFM 66.1283.02 [20] V. Šmulian, Sur la dérivabilité de la norme dans l’espace de Banach, C. R. (Doklady) Acad. Sci. URSS (N. S.) 27 (1940), 643 – 648 (French). · Zbl 0023.32604 [21] A. E. Taylor, The extension of linear functionals, Duke Math. J. 5 (1939), 538 – 547. · Zbl 0022.05402 [22] A. E. Taylor, Derivatives in the calculus, Amer. Math. Monthly 49 (1942), 631 – 642. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.