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On infinite -dimensional linear spaces. (English) Zbl 0061.24301


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[1] B. H. Arnold, Rings of operators on vector spaces, Ann. of Math. (2) 45 (1944), 24 – 49. · Zbl 0060.26904 · doi:10.2307/1969075
[2] S. Banach, Théorie des opérations linéaires, Warsaw, 1932.
[3] Garrett Birkhoff, Lattice theory, American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1961. Revised ed.
[4] R. P. Boas Jr. and J. W. Tukey, A note on linear functionals, Bull. Amer. Math. Soc. 44 (1938), no. 8, 523 – 528.
[5] M. Eidelheit, On isomorphisms of rings of linear operators, Studia Math. 9 (1940), 97 – 105 (English, with Ukrainian summary). · Zbl 0061.25301
[6] G. Fichtenholz, Sur les fonctionelles linéaires continues au sens generalisé, Rec. Math. (Mat. Sbornik) N.S. vol. 4 (1938) pp. 193-213. · Zbl 0020.13401
[7] Georg Hamel, Eine Basis aller Zahlen und die unstetigen Lösungen der Funktionalgleichung: \?(\?+\?)=\?(\?)+\?(\?), Math. Ann. 60 (1905), no. 3, 459 – 462 (German). · doi:10.1007/BF01457624
[8] F. Hausdorff, Zur Theorie der linearen metrischen Räume, J. Reine Angew. Math. vol. 167 (1932) pp. 294-311.
[9] D. H. Hyers, A note on linear topological spaces, Bull. Amer. Math. Soc. 44 (1938), no. 2, 76 – 80. · Zbl 0018.27702
[10] O. D. Kellogg, Foundations of potential theory, Berlin, 1929.
[11] H. Kober, A theorem on Banach spaces, Compositio Math. 7 (1939), 135 – 140.
[12] A. Kolmogoroff, Zur Normierbarkeit eines allgemeinen topologischen linearen Raumes, Studia Mathematica vol. 5 (1935) pp. 29-33.
[13] M. Krein and V. Šmulian, On regulary convex sets in the space conjugate to a Banach space, Ann. of Math. (2) 41 (1940), 556 – 583. · doi:10.2307/1968735
[14] Edgar R. Lorch, On a calculus of operators in reflexive vector spaces, Trans. Amer. Math. Soc. 45 (1939), no. 2, 217 – 234. · Zbl 0020.30701
[15] H. Löwig, Über die Dimension linearer Räume, Studia Mathematica vol. 5 (1934) pp. 18-23.
[16] George W. Mackey, Isomorphisms of normed linear spaces, Ann. of Math. (2) 43 (1942), 244 – 260. · Zbl 0061.24210 · doi:10.2307/1968868
[17] George W. Mackey, On infinite dimensional linear spaces, Proc. Nat. Acad. Sci. U.S.A. 29 (1943), 216 – 221. · Zbl 0061.24211
[18] George W. Mackey, On convex topological linear spaces, Proc. Nat. Acad. Sci. U. S. A. 29 (1943), 315 – 319 and Erratum 30,24.
[19] George W. Mackey, Equivalence of a problem in measure theory to a problem in the theory of vector lattices, Bull. Amer. Math. Soc. 50 (1944), 719 – 722. · Zbl 0060.13402
[20] S. Mazur, Über konvexe Mengen in linearen normierten Räumen, Studia Mathematica vol. 4 (1933) pp. 70-84.
[21] John von Neumann, On complete topological spaces, Trans. Amer. Math. Soc. 37 (1935), no. 1, 1 – 20. · Zbl 0011.16403
[22] G. Sirvint, Espace de fonctionnelles linéaires, C. R. (Doklady) Acad. Sci. URSS (N.S.) 26 (1940), 123 – 126 (French). · Zbl 0023.13003
[23] Marshall Harvey Stone, Linear transformations in Hilbert space, American Mathematical Society Colloquium Publications, vol. 15, American Mathematical Society, Providence, RI, 1990. Reprint of the 1932 original. · Zbl 0005.40003
[24] John W. Tukey, Convergence and Uniformity in Topology, Annals of Mathematics Studies, no. 2, Princeton University Press, Princeton, N. J., 1940. · Zbl 0025.09102
[25] S. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math. vol. 16 (1930) pp. 140-150.
[26] John V. Wehausen, Transformations in linear topological spaces, Duke Math. J. 4 (1938), no. 1, 157 – 169. · Zbl 0019.12302 · doi:10.1215/S0012-7094-38-00412-0
[27] A. Weil, L’integration dans les groupes topologiques et ses applications, Paris, 1938.
[28] L. R. Wilcox, Modularity in the theory of lattices, Ann. of Math. (2) 40 (1939), no. 2, 490 – 505. · Zbl 0021.10803 · doi:10.2307/1968934
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