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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An example of Fréchet space, not Montel, without infinite-dimensional normable subspaces
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by Juan C. Díaz
Proc. Amer. Math. Soc. 96 (1986), 721
DOI: https://doi.org/10.1090/S0002-9939-1986-0826509-7

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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Bibliographic 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