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A theorem of the Hahn-Banach type for linear transformations
Author:
Leopoldo Nachbin
Journal:
Trans. Amer. Math. Soc. 68 (1950), 28-46
MSC:
Primary 46.3X
MathSciNet review:
0032932
Full-text PDF Free Access
References |
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Additional Information
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F. Arens and J.
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continuous functions over a compact Hausdorff space, Trans. Amer. Math. Soc. 62 (1947), 499–508. MR 0022999
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- [1]
- R. F. Arens and J. L. Kelley, Characterizations of the space of continuous functions over a compact Hausdorff space, Trans. Amer. Math. Soc. vol. 62 (1947) pp. 499-508. MR 0022999 (9:291b)
- [2]
- S. Banach, Théorie des opérations linéaires, Warsaw, 1932.
- [3]
- I. S. Cohen, On non-Archimedean normed spaces, Indagationes Mathematicae vol. 10 (1948) pp. 244-249. MR 0025683 (10:48a)
- [4]
- J. Dieudonné, Sur le théorème de Hahn-Banach, Revue Scientifique vol. 79 (1941) pp. 642-643. MR 0013223 (7:124d)
- [5]
- -, La dualité dans les espaces vectoriels topologiques, Ann. École Norm. vol. 59 (1942) pp. 107-139. MR 0011532 (6:178g)
- [6]
- R. Godement, Les fonctions de type positif et la théorie des groupes, Trans. Amer. Math. Soc. vol. 63 (1948) pp. 1-84. MR 0023243 (9:327b)
- [7]
- S. Kakutani, Concrete representations of abstract
-spaces, Ann. of Math. vol. 42 (1941) pp. 994-1024. MR 0005778 (3:205g)
- [8]
- M. Krein and S. Krein, Sur l'espace des fonctions continues definies sur un bicompact de Hausdorff et ses sousespaces semiordonnés, Rec. Math. (Mat. Sbornik) N.S. vol. 13 (1943) pp. 1-37. MR 0012209 (6:276a)
- [9]
- M. Krein and D. Milman, On the extreme points of regularly convex sets, Studia Mathematica vol. 9 (1940) pp. 133-138. MR 0004990 (3:90a)
- [10]
- S. Lefschetz, Algebraic topology, Amer. Math. Soc. Colloquium Publications, vol. 27, New York, 1942. MR 0007093 (4:84f)
- [11]
- B.de Sz. Nagy, Sur les lattis linéaires de dimension finie, Comment. Math. Helv. vol. 17 (1945) pp. 209-213. MR 0013220 (7:124a)
- [12]
- F. Riesz, Sur quelques notions fondamentales dans la théorie générale des opérations linéaires, Ann. of Math. vol. 41 (1940) pp. 174-206. MR 0000902 (1:147d)
- [13]
- M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. vol. 41 (1937) pp. 375-481. MR 1501905
- [14]
- -, A general theory of spectra, I and II, Proc. Nat. Acad. Sci. U.S.A. vol. 26 (1940) pp. 280-283, vol. 27 (1941) pp. 83-87. MR 0002023 (1:338e)
- [15]
- -, Boundedness properties in function-lattices, Canadian Journal of Mathematics vol. 1 (1949) pp. 176-186. MR 0029091 (10:546a)
- [16]
- A. Youdine, Solution de deux problèmes de la théorie des espaces semiordonnés, C. R. (Doklady) Acad. Sci. URSS. vol. 27 (1939) pp. 418-422.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1950-0032932-3
PII:
S 0002-9947(1950)0032932-3
Article copyright:
© Copyright 1950 American Mathematical Society
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