Projective and injective limits of weakly compact sequences of locally convex spaces

Hikosaburo KOMATSU

doi:10.2969/jmsj/01930366

Hikosaburo KOMATSU

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JOURNAL FREE ACCESS

1967 Volume 19 Issue 3 Pages 366-383

DOI https://doi.org/10.2969/jmsj/01930366

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Published: 1967 Received: February 14, 1967 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) N. Bourbaki, Espaces Vectoriels Topologiques, Chapitres III-V, Hermann, Paris, 1955.
2) F. E, Browder, Functional analysis and partial differential equations, Math. Ann., 138 (1959), 55-79 and 145 (1962), 81-226.
3) J. Dieudonné and L. Schwartz, La dualité dans les espaces (F) et (LF), Ann. Inst. Fourier, 1 (1949), 61-101.
4) N. Dunford and J, T. Schwartz, Linear Operators, Part I, Interscience, New York, 1958.
5) A. Grothendieck, Sur les espaces (F) et (DF), Summa Brasil. Math., 3 (1954), 57-123.
6) A. Grothendieck, Produits Tensoriels Topologiques et Espaces Nucléaires, Mem. Amer. Math. Soc., No. 16, 1955.
7) A. Grothendieck, Espaces Vectoriels Topologiques, Univ. de São Paulo, São Paulo, 1954,
8) G. Köthe, Topologische Lineare Räume I, Springer, Berlin, 1960.
9) H. Komatsu, Resolutions by hyperfunctions of sheaves of solutions of differential equations with constant coefficients, to appear in Math. Ann.
10) A. Martineau, Les hyperfonctions de M. Sato, Sém, Bourbaki, 13 (1960-61), No 214.
11) V. Pták, Completeness and the open mapping theorem, Bull. Soc. Math. France, 86 (1958), 41-74.
12) D. A. Raikov, On two classes of locally convex spaces important in applications, Trudy Sem. Funct. Anal. at Voronez, 5 (1957), 22-34 (Russian).
13) D. A. Raikov, Completely continuous spectra of locally convex spaces, Trudy Moskov. Mat. Obšc., 7 (1958), 413-438 (Russian).
14) J. P. Serre, Un théorème de dualité, Comm. Math, Helv., 29 (1955), 9-26.
15) J. S. e Silva, Su certi classi spazi localmente convessi importanti per le applica-zioni, Rend. Mat, e Appl., 14 (1955), 388-410.
16) J. Wloka, Funktionalanalysis in nicht normierte Räumen, Lecture Note at Univ. Heidelberg, 1966.
17) B. M. Makarov, On inductive limits of normed spaces, Dokl. Akad. Nauk SSSR, 119 (1958), 1092-1094 and Vestnik Leningrad. Univ., 13 (1965), 50-58 (Russian),
18) D.A. Raikov, A criterion of completeness of locally convex spaces, Uspehi Mat. Nauk, 14 (85) (1959), 223-229 (Russian).

Right : [1] N. Bourbaki, Espaces Vectoriels Topologiques, Chapitres III-V, Hermann, Paris, 1955.
[2] F. E, Browder, Functional analysis and partial differential equations, Math. Ann., 138 (1959), 55-79 and 145 (1962), 81-226.
[3] J. Dieudonné and L. Schwartz, La dualité dans les espaces (F) et (LF), Ann. Inst. Fourier, 1 (1949), 61-101.
[4] N. Dunford and J, T. Schwartz, Linear Operators, Part I, Interscience, New York, 1958.
[5] A. Grothendieck, Sur les espaces (F) et (DF), Summa Brasil. Math., 3 (1954), 57-123.
[6] A. Grothendieck, Produits Tensoriels Topologiques et Espaces Nucléaires, Mem. Amer. Math. Soc., No. 16, 1955.
[7] A. Grothendieck, Espaces Vectoriels Topologiques, Univ. de São Paulo, São Paulo, 1954,
[8] G. Köthe, Topologische Lineare Räume I, Springer, Berlin, 1960.
[9] H. Komatsu, Resolutions by hyperfunctions of sheaves of solutions of differential equations with constant coefficients, to appear in Math. Ann.
[10] A. Martineau, Les hyperfonctions de M. Sato, Sém, Bourbaki, 13 (1960-61), No 214.
[11] V. Pták, Completeness and the open mapping theorem, Bull. Soc. Math. France, 86 (1958), 41-74.
[12] D. A. Raikov, On two classes of locally convex spaces important in applications, Trudy Sem. Funct. Anal. at Voronez, 5 (1957), 22-34 (Russian).
[13] D. A. Raikov, Completely continuous spectra of locally convex spaces, Trudy Moskov. Mat. Obšc., 7 (1958), 413-438 (Russian).
[14] J. P. Serre, Un théorème de dualité, Comm. Math, Helv., 29 (1955), 9-26.
[15] J. S. e Silva, Su certi classi spazi localmente convessi importanti per le applicazioni, Rend. Mat, e Appl., 14 (1955), 388-410.
[16] J. Wloka, Funktionalanalysis in nicht normierte Räumen, Lecture Note at Univ. Heidelberg, 1966.
[17] B. M. Makarov, On inductive limits of normed spaces, Dokl. Akad. Nauk SSSR, 119 (1958), 1092-1094 and Vestnik Leningrad. Univ., 13 (1965), 50-58 (Russian).
[18] D. A. Raikov, A criterion of completeness of locally convex spaces, Uspehi Mat. Nauk, 14 (85) (1959), 223-229 (Russian).

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