Geodesic
Quotient Spaces Without Bases in Nuclear Frechet Spaces
Canadian journal of mathematics, Tome 30 (1978) no. 6, pp. 1296-1305

Voir la notice de l'article provenant de la source Cambridge University Press

The first example of a nuclear Fréchet space without a basis was given by B. S. Mitiagin and N. M. Zobin [9; 10]. The question of existence of subspaces without bases in nuclear Fréchet spaces was recently settled in papers by P. Djakov and B. S. Mitiagin [2] and Ed Dubinsky [5]. In this paper we consider the analogous question for quotient spaces. As in the case of subspaces we obtain a complete solution to the problem. 
Dubinsky, Ed; Mitiagin, Boris. Quotient Spaces Without Bases in Nuclear Frechet Spaces. Canadian journal of mathematics, Tome 30 (1978) no. 6, pp. 1296-1305. doi: 10.4153/CJM-1978-106-9
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[1] 1. Bessaga, Cz. and Pefczyriski, A., Wfasnosci baa w przestrzcniach typu B, Prace MatematyczneS (1959), 123–142. Google Scholar

[2] 2. Plamen, Djakov and Boris, Mitiagin, Modified construction of nuclear Fréchet spaces without basis, J. Functional Anal. 23 (1976), 415–433. Google Scholar

[3] 3. Dubinsky, Ed, Perfect Fréchet spaces, Math. Ann. 174 (1967), 186–194. Google Scholar

[4] 4, Dubinsky, Ed Concrete subs paces of nuclear Fréchet spaces, Studia Math. 52 (1975), 209–219. Google Scholar

[5] 5. Dubinsky, Ed Subspaces without bases in nuclear Fréchet spaces, J. Functional Anal. 26 (1977), 121–130. Google Scholar

[6] 6. Dubinsky, Ed and Robinson, W. B., Quotient spaces of (s) with basis, Studia Math. Google Scholar

[7] 7. Johnson, W. B. and Rosenthal, H. P., On ta*-basic sequences and their applications to the study of Banach spaces, Studia Math. 4-1 (1972), 77–92. Google Scholar

[8] 8. Kothe, G., Topological vector spaces I (Springer-Verlag, New York, 1969). Google Scholar

[9] 9. Mitiagin, B. S. and X, Zobin, M., Contre-exemple à l'existence d'une base dans un espace de Fréchet nucléaire, C. R. Acad. Sci. Paris, ser. A 279 (1974). Google Scholar

[10] 10. Zobin, N. M. and Mitiagin, B. S., Examples of nuclear Fréchet spaces without basis, cional. Anal, i Prilozen. 8 (1974), 35–47. Google Scholar

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