Topological structures in ordered linear spaces

Ichiro AMEMIYA; Tuyosi MORI

doi:10.2969/jmsj/00910131

Ichiro AMEMIYA, Tuyosi MORI

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JOURNAL FREE ACCESS

1957 Volume 9 Issue 1 Pages 131-142

DOI https://doi.org/10.2969/jmsj/00910131

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Published: 1957 Received: October 31, 1955 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) I. Amemiya: On the equi-continuity in semi-ordered linear spaces. Proc. Japan Acad., 27 (1951), p. 275.
2) I. Amemiya: A generalization of Riesz-Fischer's theorem. J. Math. Soc. Japan, 5 (1953), pp. 353-354.
3) N. Bourbaki : Intégration, chap. II Espaces de Riesz. Paris, 1952.
4) N. Bourbaki: Algèbre, chap. VI Groupes et corps ordonnés. Paris, 1952.
5) N. Bourbaki: Espaces vectoriels topologiques, chap. IV La dualité dans les espaces vectoriels topologiques. Paris, 1955.
6) J. L. B. Cooper: Coordinated linear spaces. Proc. London Math. Soc., Ser. 3, 3 (1953), pp. 305-327.
7) A. Grothendieck: Critère des compacité dans les espaces fonctionels généraux. Amer. J. Math., 74 (1952), pp. 168-186.
8) I. Halperin and H. Nakano: Discrete semi-ordered linear spaces. Canadian J. Math., 3 (1951), pp. 293-298.
9) G. Köthe: Neubegründung der Theorie der vollkommenen Räume. Math. Nachr., 4 (1951), pp. 70-80.
10) H. Nakano: Stetige lineare Funktionale auf dem teilweisegeordneten Modul. J. Fac. Sci. Imp. Univ. Tokyo, 4 (1942), pp. 201-382.
11) H. Nakano: Modulared semi-ordered linear spaces. Tokyo, 1950.
12) H. Nakano: Modern spectral theory. Tokyo, 1950.
13) H. Nakano: Linear topologies on semi-ordered linear spaces. J. Fac. Sci. Hokkaido Univ., Ser. 1, 12 (1953), pp. 87-104.
14) J. v. Neumann: On rings of operators III. Ann. of Math., 41 (1940), pp. 94-161.

Right : [1] I. Amemiya: On the equi-continuity in semi-ordered linear spaces. Proc. Japan Acad., 27 (1951), p. 275.
[2] I. Amemiya: A generalization of Riesz-Fischer's theorem. J. Math. Soc. Japan, 5 (1953), pp. 353-354.
[3] N. Bourbaki : Intégration, chap. II Espaces de Riesz. Paris, 1952.
[4] N. Bourbaki: Algèbre, chap. VI Groupes et corps ordonnés. Paris, 1952.
[5] N. Bourbaki: Espaces vectoriels topologiques, chap. IV La dualité dans les espaces vectoriels topologiques. Paris, 1955.
[6] J. L. B. Cooper: Coordinated linear spaces. Proc. London Math. Soc., Ser. 3, 3 (1953), pp. 305-327.
[7] A. Grothendieck: Critère des compacité dans les espaces fonctionels généraux. Amer. J. Math., 74 (1952), pp. 168-186.
[8] I. Halperin and H. Nakano: Discrete semi-ordered linear spaces. Canadian J. Math., 3 (1951), pp. 293-298.
[9] G. Köthe: Neubegründung der Theorie der vollkommenen Räume. Math. Nachr., 4 (1951), pp. 70-80.
[10] H. Nakano: Stetige lineare Funktionale auf dem teilweisegeordneten Modul. J. Fac. Sci. Imp. Univ. Tokyo, 4 (1942), pp. 201-382.
[11] H. Nakano: Modulared semi-ordered linear spaces. Tokyo, 1950.
[12] H. Nakano: Modern spectral theory. Tokyo, 1950.
[13] H. Nakano: Linear topologies on semi-ordered linear spaces. J. Fac. Sci. Hokkaido Univ., Ser. 1, 12 (1953), pp. 87-104.
[14] J. v. Neumann: On rings of operators III. Ann. of Math., 41 (1940), pp. 94-161.

Date of correction: August 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

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