Locally convex lattices

Itizo KAWAI

doi:10.2969/jmsj/00930281

Itizo KAWAI

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JOURNAL FREE ACCESS

1957 Volume 9 Issue 3 Pages 281-314

DOI https://doi.org/10.2969/jmsj/00930281

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Published: 1957 Received: January 24, 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 and T. Mori, Topological structures in ordered linear spaces, J. Math. Soc. Japan, 9 (1957) pp. 131-142.
2) G. Birkhoff, Lattice theory (Revised edition), Amer. Math. Soc. Colloq. Publ., 25, 1949.
3) N. Bourbaki, Sur certains espaces vectoriels topologiques, Ann. Inst. Fourier, 2 (1950) pp. 5-16.
4) N. Bourbaki, Espaces vectoriels topologiques, chap. 2, Actual. Scient. et Ind., Paris, 1953.
5) N. Bourbaki, Espaces vectoriels topologiques, chap. 3, 4, Actual. Scient. et Ind., Paris, 1955.
6) N. Bourbaki, Topologie générale, chap. 1, Actual. Scient, et Ind., Paris, 1951.
7) N. Bourbaki, Integration, chap. 3, Actual. Scient. et Ind., Paris, 1952.
8) J. Dieudonné et L. Schwartz, La dualité dans les espaces (_??_) et (_??_), Ann. Inst. Fourier, 1 (1949) pp. 61-101.
9) W. F. Donoghue and K. T. Smith, On the symmetry and bounded closure of locally convex spaces, Trans. Amer. Math. Soc., 73 (1952) pp. 321-344.
10) A. Grothendieck, Critères de compacité dans les espaces fonctionnels généraux, Amer. J. Math., 74 (1952) pp. 168-186.
11) I. Halperin and H. Nakano, Discrete semi-ordered linear spaces, Canadian J. Math., 3 (1951) pp. 293-298.
12) L. Kantorovitch, Lineare halbgeordnete Räume, Math. Sbornik, 2 (44), (1937) pp. 121-168.
13) I. Kawai, On the metrically complete extension of a normed vector lattice, Rep. Liberal Arts Fac. Shizuoka Univ., B, 2 (1951) pp. 1-17.
14) J. L. Kelley, Convergence in topology, Duke Math. J., 17 (1950) pp. 277-283.
15) L. H. Loomis, An introduction to abstract harmonic analysis, New York, 1953.
16) G. W. Mackey, On infinite-dimensional linear spaces, Trans. Amer. Math. Soc., 57 (1945) pp. 155-207.
17) G. W. Mackey, On convex topological spaces, Trans. Amer. Math. Soc., 60 (1946) pp. 519-537.
18) E. A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. (11), New York, 1952.
19) H. Nakano, Modulared semi-ordered linear spaces (Tokyo Math. Book Ser. 1), Tokyo, 1950.
20) H. Nakano, Modern Spectral theory (Tokyo Math. Book Ser. 2), Tokyo, 1950.
21) H. Nakano, Linear topologies on semi-ordered linear spaces, J. Fac. Sci. Hokkaido Univ., 1. 12 (1953) pp. 87-104.
22) T. Ogasawara, Lattice theory (2), (in Japanese), Tokyo, 1947.
23) M. Nakamura, Notes on Banach Space (9): The Vitali-Hahn Saks theorems and K-spaces, Tohoku Math. J., 1 (1949) pp. 100-108.
24) M. Nakamura, Notes on Banach Space (11): Banach Lattices with Positive Bases, Tohoku Math. J., 2(1950) pp. 135-141.
25) O. Takenouchi, Sur les espaces linéaires localement convexes, Math. J. Okayama Univ., 2 (1952) pp. 57-84.

Right : [1] I. Amemiya and T. Mori, Topological structures in ordered linear spaces, J. Math. Soc. Japan, 9 (1957) pp. 131-142.
[2] G. Birkhoff, Lattice theory (Revised edition), Amer. Math. Soc. Colloq. Publ., 25, 1949.
[3] N. Bourbaki, Sur certains espaces vectoriels topologiques, Ann. Inst. Fourier, 2 (1950) pp. 5-16.
[4] N. Bourbaki, Espaces vectoriels topologiques, chap. 2, Actual. Scient. et Ind., Paris, 1953.
[5] N. Bourbaki, Espaces vectoriels topologiques, chap. 3, 4, Actual. Scient. et Ind., Paris, 1955.
[6] N. Bourbaki, Topologie générale, chap. 1, Actual. Scient, et Ind., Paris, 1951.
[7] N. Bourbaki, Integration, chap. 3, Actual. Scient. et Ind., Paris, 1952.
[8] J. Dieudonné et L. Schwartz, La dualité dans les espaces (ℑ) et (_??_ℑ), Ann. Inst. Fourier, 1 (1949) pp. 61-101.
[9] W. F. Donoghue and K. T. Smith, On the symmetry and bounded closure of locally convex spaces, Trans. Amer. Math. Soc., 73 (1952) pp. 321-344.
[10] A. Grothendieck, Critères de compacité dans les espaces fonctionnels généraux, Amer. J. Math., 74 (1952) pp. 168-186.
[11] I. Halperin and H. Nakano, Discrete semi-ordered linear spaces, Canadian J. Math., 3 (1951) pp. 293-298.
[12] L. Kantorovitch, Lineare halbgeordnete Räume, Math. Sbornik, 2 (44), (1937) pp. 121-168.
[13] I. Kawai, On the metrically complete extension of a normed vector lattice, Rep. Liberal Arts Fac. Shizuoka Univ., B, 2 (1951) pp. 1-17.
[14] J. L. Kelley, Convergence in topology, Duke Math. J., 17 (1950) pp. 277-283.
[15] L. H. Loomis, An introduction to abstract harmonic analysis, New York, 1953.
[16] G. W. Mackey, On infinite-dimensional linear spaces, Trans. Amer. Math. Soc., 57 (1945) pp. 155-207.
[17] G. W. Mackey, On convex topological spaces, Trans. Amer. Math. Soc., 60 (1946) pp. 519-537.
[18] E. A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. (11), New York, 1952.
[19] H. Nakano, Modulared semi-ordered linear spaces (Tokyo Math. Book Ser. 1), Tokyo, 1950.
[20] H. Nakano, Modern Spectral theory (Tokyo Math. Book Ser. 2), Tokyo, 1950.
[21] H. Nakano, Linear topologies on semi-ordered linear spaces, J. Fac. Sci. Hokkaido Univ., 1. 12 (1953) pp. 87-104.
[22] T. Ogasawara, Lattice theory (2), (in Japanese), Tokyo, 1947.
[23] M. Nakamura, Notes on Banach Space (9): The Vitali-Hahn Saks theorems and K-spaces, Tohoku Math. J., 1 (1949) pp. 100-108.
[24] M. Nakamura, Notes on Banach Space (11): Banach Lattices with Positive Bases, Tohoku Math. J., 2 (1950) pp. 135-141.
[25] O. Takenouchi, Sur les espaces linéaires localement convexes, Math. J. Okayama Univ., 2 (1952) pp. 57-84.

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