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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Fréchet spaces with nuclear Köthe quotients


Authors: Steven F. Bellenot and Ed Dubinsky
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0667161-4
Article copyright: © Copyright 1982 American Mathematical Society