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Nuclear and product spaces, Baire-like spaces, and the strongest locally convex topology. (English) Zbl 0243.46011

MSC:
46A03 General theory of locally convex spaces
46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.)
46A08 Barrelled spaces, bornological spaces
46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
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References:
[1] Amemiya, I., K?muro, Y.: Über nicht-vollständige Montelräume, Math. Ann.177, 273-277 (1968). · Zbl 0157.43903 · doi:10.1007/BF01350719
[2] Bourbaki, N.: Eléments de mathématique, Livre V. Espaces vectoriels topologiques, Act. Sci. et Ind. Vol. 1229 (1955). · Zbl 0067.08302
[3] De Wilde, M.: Quelques théorèmes d’extension de fonctionnelles linéaires. Bull. Soc. Royale Sc. de Liége, 9-10, 551-557 (1966).
[4] – Houet, C.: On increasing sequences of absolutely convex sets in locally convex spaces. Math. Ann. (to appear). · Zbl 0203.42802
[5] Diedonné, J.: Sur les propriétés permanence de certains espaces vectoriels topologiques, Ann. Soc. Polon. Math.25, 50-55 (1952). · Zbl 0049.08202
[6] Diestel, J., Morris, S., Saxon, S.: Varieties of locally convex topological vector spaces. Bull. Amer. Math. Soc.77, 799-803 (1971). · Zbl 0219.46002 · doi:10.1090/S0002-9904-1971-12811-2
[7] – – – Varieties of linear topological spaces. Trans. Amer. Math. Soc. (to appear).
[8] Edwards, R. E.: Functional analysis. New York: Holt, Rinehart, and Winston, 1965. · Zbl 0182.16101
[9] Grothendieck, A.: Espaces vectoriels topologiques, 3rd ed. (Sao Paulo, Sociedade de Mathematica de Sao Paulo, 1964). · Zbl 0316.46001
[10] – Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. No.16 (1955).
[11] Horváth: Topological vector spaces and distributions, Vol. I, Reading, Massachusetts: Addison-Wesley, 1966.
[12] Husain, T.: The open mapping and closed graph theorems in topological vector spaces, Oxford: Oxford University Press, 1965. · Zbl 0124.06301
[13] Kaplan, S.: Cartesian products of reals. Amer. J. Math.74, 936-954 (1952). · Zbl 0049.35402 · doi:10.2307/2372236
[14] Kelley, J., Namioka, I.: Linear topological spaces, Princeton: D. Van Nostrand Company, Inc. 1963. · Zbl 0115.09902
[15] K?mura, T., K?mura, Y.: Über die Einbettung der nuclearen Räume in (s)A. Math. Ann.162, 284-288 (1966). · Zbl 0156.13402 · doi:10.1007/BF01360917
[16] Köthe, G.: Die Bildräume abgeschlossener Operatoren. J. von Reine und Angewandte Math.232, 110-111 (1968). · Zbl 0157.21003 · doi:10.1515/crll.1968.232.110
[17] ?? Topologische lineare Räume, Vol. I, Berlin-Göttingen-Heidelberg Springer 1960.
[18] Levin, M., Saxon, S.: A note on the inheritance of properties of locally convex spaces by subspaces of countable condimension. Proc. Amer. Math. Soc.,29, 97-102 (1971). · Zbl 0212.14104 · doi:10.1090/S0002-9939-1971-0280973-2
[19] Oxtoby, J.: Cartesian products of Baire spaces. Fund. Math.49, 157-166 (1961). · Zbl 0113.16402
[20] Pták, V.: Completeness and the open mapping theorem, Bull. Soc. Math. Fr.86, 41-74 (1958). · Zbl 0082.32502
[21] Robertson, A. P., Robertson, W.: On the closed graph theorem. Proc. Glasg. Math. Assoc.3, 9-12 (1956). · Zbl 0073.08702 · doi:10.1017/S2040618500033372
[22] Saxon, S.: Basis cone base theory. Florida State University dissertation (1969).
[23] ?? Levin, M.: Every countable-codimensional subspace of a barrelled space is barrelled. Proc. A.M.S.29, 91-96 (1971). · Zbl 0212.14105 · doi:10.1090/S0002-9939-1971-0280972-0
[24] – (LF)-spaces, quasi-Baire spaces, and the strongest locally convex topology (to appear). · Zbl 0575.46002
[25] – Embedding nuclear spaces in products of an arbitrary Banach space, Proc. Amer. Math. Soc. (to appear). · Zbl 0257.46006
[26] Schwartz, L.: Functional analysis, New York University, Courant Institute of Mathematical Sciences (1964). · Zbl 0163.23901
[27] Valdivia, M.: Absolutely convex sets in barrelled spaces. Ann. Inst. Fourier, Grenoble21, (2) 3-13 (1971). · Zbl 0205.40904
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