Fréchet spaces with nuclear Köthe quotients

Bellenot, Steven F.; Dubinsky, Ed

doi:10.1090/S0002-9947-1982-0667161-4

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 with a continuous norm is shown to have a quotient with a continuous norm and a basis. If, in addition, can be chosen to be nuclear, we say that 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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