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 | References | Similar Articles | Additional Information
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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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1982-0667161-4
Article copyright:
© Copyright 1982
American Mathematical Society