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A Generalization of the Hahn-Banach Theorem

Published online by Cambridge University Press:  22 January 2016

Takashi Ono
Takashi Ono*
Affiliation:
Mathematical Institute, Nagoya University
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Recently the Hahn-Banach theorem for normed spaces over non-archimedean valued fields was treated by A. F. Monna [1], L S. Cohen [2], A. W. Ingleton [3], and the writer [4]. In [3] and [4] very essential use was made of an idea of L. Nachbin [5]

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 6 , October 1953 , pp. 171 - 176
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1953

References

[1] Monna, A. F., Sur les espaces linéaires normes, III. Indag. Math., 8 (1946).Google Scholar
[2] Cohen, I. S., On non-Archimedean normed spaces, Indag. Math., 10 (1948).Google Scholar
[3] Ingleton, A. W., The Hahn-Banach theorem for non-Archimedean valued fields, Proc. Cambridge Phil. Soc, 48 (1952).CrossRefGoogle Scholar
[4] Ono, T., On the extension property of normed spaces over fields with non-archimedean valuations, Journ. Math. Soc. Japan., 5 (1953).Google Scholar
[5] Nachbin, L., A theorem of the Hahn-Banach type for linear transformations, Trans. Amer. Math. Soc, 68 (1950).CrossRefGoogle Scholar
[6] Chevalley, C., Sur la théorie du corps de classes dans les corps finis et les corps locaux, Journ. of Coll. of Sciences, Tokyo, 2 (1933).Google Scholar
[7] F, O.. Schilling, G., The theory of valuations, New York (1950).Google Scholar
[8] Satake, I., Two remarks on valuation theory, Math. Reports of Tôdai-Kyôyôgakubu, 2 (1951) (in Japanese).Google Scholar
[9] Banach, S., Theorie des opérations linéaires, Warsow (1932).Google Scholar
[10] Bohnenblust, H.F. and Sobczyk, A., Extensions of functionals on complex linear spaces, Bullet. Amer. Math. Soc, (1938).CrossRefGoogle Scholar
[11] Deuring, M., Algebren, Ergeb, Math., 4 (1935).Google Scholar
[12] Mackey, G. W., Isomorphisms of normed linear spaces, Ann. of Math., 43 (1942).Google Scholar
[13] Kakutani, S., Lattices and rings connected with Banach spaces, Isô-Sûgaku 5 (1943) (in Japanese).Google Scholar
[14] Abe, M., Projective transformation groups over non-commutative fields, Sijô-Sûgaku-Danwakai, 240 (1942) (in Japanese).Google Scholar
[15] Artin, E., Algebraic Numbers and algebraic functions, Princeton (1951).Google Scholar
[16] Hille, E., Functional analysis and semi-groups, New York (1948).Google Scholar
[17] Eidelheit, M., On isomorphisms of rings of linear operators, Stud. Math., 9 (1939).Google Scholar
[18] Kawada, Y., Über den Operatorenring Banachscher Räume, Proc. Imp. Acad. Tokyo., 19 (1943).Google Scholar