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Montel Subspaces in the Countable Projective Limits of Lp(μ)-Spaces

Published online by Cambridge University Press:  20 November 2018

J. C. Díaz
J. C. Díaz*
Affiliation:
Cátedra de Matemáticas. E.T.S.I.A., 14004 Cordoba, Spain
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Abstract

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Let us suppose one of the following conditions: (a) p ≧ 2 and F is a closed subspace of a projective limit (b) p = 1 and F is a complemented subspace of an echelon Köthe space of order 1, Λ(X,β,μ,gk); and (c) 1 > p > 2 and F is a quotient of a countable product of Lp(μn) spaces. Then, F is Montel if and only if no infinite dimensional subspace of F is normable.

Keywords

46A14
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 2 , 01 June 1989 , pp. 169 - 176
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Beauzamy, B., Introduction to Banach spaces and their geometry, Mathematics Studies, North- Holland, 1968.Google Scholar
2. Bellenot, S. F., Basic sequences in non-Schwartz Fréchet spaces, Trans. Amer. Math. Soc. 258 (1980), No. 1, 199–216.Google Scholar
3. Bellenot, S. F. and Dubinsky, E., Fréchet spaces with nuclear Kôthe quotients, Trans. Amer. Math. Soc. 273,579–594 (1982).Google Scholar
4. Diaz, J. C., An example of Fréchet space, not Montel, without infinite dimensional normable subspaces, Proc. Amer. Math. Soc. 96, 4, 721 (1986).Google Scholar
5. Dieudonne, J. and Gomes, A. P., Sur certain espaces vectoriels topologiques, C.R. Acad. Sci., Paris 230,1129–1130(1957).Google Scholar
6. Kadec, M. I. and Pelczynski, A., Bases, lacunary sequences and complemented subspaces in the spaces LP, Studia Math. 21(1962), 161–176.Google Scholar
7. Kôthe, G., Topological Vector Spaces I, II, Springer Verlag, Berlin 1969.Google Scholar
8. Lindenstrauss, J. and Tzafiri, L., Classical Banach Spaces I., Surveys in Math. Springer Verlag, 1979.Google Scholar
9. Lopez-Molina, J. A., The dual and bidual of an echelon Kôthe space, Collec. Math. 31,2 (1980), 159–191.Google Scholar
10. Lopez-Molina, J. A. and Lopez-Pellicer, , Consequences of the Dunford-Pettis property in the echelon Kôthe spaces, Preprint.Google Scholar
11. Orihuela, J., Pointwise compactness in spaces of continuous functions, To appear in Journal London Math. Soc.Google Scholar
12. Rosenthal, H. P., A characterization of Banach spaces containing lx, Proc. Nat. Acad. Sci. USA, 71, No. 6, 2411-2413, June 1974.Google Scholar
13. Schaefer, H. H., Topological vector spaces, Springer Verlag, 1970.Google Scholar
14. Valdivia, M., Topics in locally convex spaces, North-Holland, 1982.Google Scholar