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Quotient Spaces Without Bases in Nuclear Frechet Spaces

Published online by Cambridge University Press:  20 November 2018

Ed Dubinsky  and
Boris Mitiagin
Ed Dubinsky
Affiliation:
Clarkson College of Technology, Potsdam, New York
Boris Mitiagin
Affiliation:
Clarkson College of Technology, Potsdam, New York
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1296 - 1305
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Bessaga, Cz. and Pefczyriski, A., Wfasnosci baa w przestrzcniach typu B, Prace MatematyczneS (1959), 123–142.Google Scholar
2. Plamen, Djakov and Boris, Mitiagin, Modified construction of nuclear Fréchet spaces without basis, J. Functional Anal. 23 (1976), 415–433.Google Scholar
3. Dubinsky, Ed, Perfect Fréchet spaces, Math. Ann. 174 (1967), 186–194.Google Scholar
4, Dubinsky, Ed Concrete subs paces of nuclear Fréchet spaces, Studia Math. 52 (1975), 209–219.Google Scholar
5. Dubinsky, Ed Subspaces without bases in nuclear Fréchet spaces, J. Functional Anal. 26 (1977), 121–130.Google Scholar
6. Dubinsky, Ed and Robinson, W. B., Quotient spaces of (s) with basis, Studia Math.Google Scholar
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. Kothe, G., Topological vector spaces I (Springer-Verlag, New York, 1969).Google Scholar
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. Zobin, N. M. and Mitiagin, B. S., Examples of nuclear Fréchet spaces without basis, Funkcional. Anal, i Prilozen. 8 (1974), 35–47.Google Scholar