An example of Fréchet space, not Montel, without infinite-dimensional normable subspaces
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- by Juan C. Díaz PDF
- Proc. Amer. Math. Soc. 96 (1986), 721 Request permission
Abstract:
Given $X$ a Fréchet Montel space, no infinite dimensional subspace of $X$ is normable. We show that the converse implication is not true in general. In fact we provide here a Fréchet space $X$ (moreover, $X$ is a perfect Fréchet space), which is not Montel but does not contain an infinite dimensional normable subspace.References
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J. C. Díaz, Montel subspaces in the echelon Köthe spaces (to appear).
- Steven F. Bellenot, Basic sequences in non-Schwartz Fréchet spaces, Trans. Amer. Math. Soc. 258 (1980), no. 1, 199–216. MR 554329, DOI 10.1090/S0002-9947-1980-0554329-9
- Ed Dubinsky, Perfect Fréchet spaces, Math. Ann. 174 (1967), 186–194. MR 220036, DOI 10.1007/BF01360717
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97, Springer-Verlag, Berlin-New York, 1979. Function spaces. MR 540367, DOI 10.1007/978-3-662-35347-9
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 721
- MSC: Primary 46A14
- DOI: https://doi.org/10.1090/S0002-9939-1986-0826509-7
- MathSciNet review: 826509