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An example of Fréchet space, not Montel, without infinite-dimensional normable subspaces


Author: Juan C. Díaz
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
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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 [Enhancements On Off] (What's this?)

  • [1] J. C. Díaz, Montel subspaces in the echelon Köthe spaces (to appear).
  • [2] S. F. Bellenot, Basic sequences in non-Schwartz-Fréchet spaces, Trans. Amer. Math. Soc. 258 (1980), 199-216. MR 554329 (83b:46008)
  • [3] E. Dubinsky, Perfect Fréchet spaces, Math. Ann. 174 (1967), 186-194. MR 0220036 (36:3103)
  • [4] J. Lindenstrauss and L. Tzafiri, Classical Banach spaces. I, Surveys in Math, Springer-Verlag, 1979. MR 540367 (81c:46001)

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DOI: https://doi.org/10.1090/S0002-9939-1986-0826509-7
Article copyright: © Copyright 1986 American Mathematical Society

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