Fréchet spaces with nuclear Köthe quotients
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- by Steven F. Bellenot and Ed Dubinsky PDF
- Trans. Amer. Math. Soc. 273 (1982), 579-594 Request permission
Abstract:
Each separable Fréchet non-Banach space $X$ with a continuous norm is shown to have a quotient $Y$ with a continuous norm and a basis. If, in addition, $Y$ can be chosen to be nuclear, we say that $X$ has a nuclear Köthe quotient. We obtain a (slightly technical) characterization of those separable Fréchet spaces with nuclear Köthe quotients. In particular, separable reflexive Fréchet spaces which are not Banach (and thus Fréchet Montel spaces) have nuclear Köthe quotients.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 273 (1982), 579-594
- MSC: Primary 46A12
- DOI: https://doi.org/10.1090/S0002-9947-1982-0667161-4
- MathSciNet review: 667161