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Modified construction of nuclear Frechet spaces without basis. (English) Zbl 0339.46004


MSC:

46A35 Summability and bases in topological vector spaces
46A03 General theory of locally convex spaces
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[1] Bessaga, C.; Pelczynski, A., On imbedding of nuclear spaces into the space of all infinitely differentiable functions on a straight line, Dokl. Akad. Nauk SSSR, 134, 4, 745-748 (1960), (Russian)
[2] Dubinsky, E., Perfect Fréchet spaces, Math. Ann., 174, 3, 186-194 (1967) · Zbl 0166.10403
[3] Dynin, A.; Mitiagin, B., Criterion for nuclearity in terms of approximative dimension, Bull. Acad. Pol. Sci., 8, 8, 535-540 (1960) · Zbl 0104.08504
[4] Komura, T.; Komura, Y., Über die Einbettung der nuklearen Räume in \((s)0\), Math. Ann., 162, 294 (1965-1966) · Zbl 0156.13402
[5] Mitiagin, B. S., The approximative dimension and bases in nuclear spaces, Usp. Mat. Nauk, 16, 4, 63-132 (1961), (Russian)
[6] Mitiagin, B. S.; Zobin, N. M., Contre-exemple à l’existence d’une base dans un espace de Fréchet nucléaire, C. R. Acad. Sci. Paris, ser. A, 279 (1974) · Zbl 0312.46016
[7] Pelczynski, A., Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basis, Studia Math., 40, 3, 239-243 (1971) · Zbl 0223.46019
[8] Pietsch, A., Nukleare Lokalkonvexe Räume (1965), Berlin · Zbl 0152.32302
[9] Zahariuta, V. P., On the isomorphism of the cartesian products of locally convex spaces, Studia Math., 46, 3, 201-221 (1973) · Zbl 0261.46003
[10] Zahariuta, V. P., The spaces of analytic functions of one variable on open sets and on compacta, Matem. Sborn., 82, 1, 84-98 (1970), (Russian)
[11] Zerner, M., Développement en séries de polynômes orthonormaux des fonction indéfiniment différentiables, C. R. Acad. Sci. Paris, ser. A, 268, 218 (1969) · Zbl 0189.14601
[12] Zobin, N. M.; Mitiagin, B. S., Examples of nuclear Fréchet spaces without basis, Funkcional. Anal. i Priložen., 8, 4, 35-47 (1974), (Russian)
[13] Zobin, N. M.; Mitiagin, B. S., Continuum of pairwise-nonisomorphic nuclear Fréchet spaces without basis, Sibirsk. Matem. J., 17, 2, 249-258 (1976) · Zbl 0334.46018
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