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Proceedings of the American Mathematical Society

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A note on countably normed nuclear spaces


Author: Lasse Holmström
Journal: Proc. Amer. Math. Soc. 89 (1983), 453-456
MSC: Primary 46A12
DOI: https://doi.org/10.1090/S0002-9939-1983-0715865-3
MathSciNet review: 715865
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Abstract: A modification of the Kōmura-Kōmura imbedding theorem is used to show that every countably normed nuclear space is isomorphic to a subspace of a nuclear Fréchet space with basis and a continuous norm. The space with basis can be chosen to be a quotient of $ (s)$.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0715865-3
Keywords: Nuclear Fréchet space, countably normed, nuclear Köthe space
Article copyright: © Copyright 1983 American Mathematical Society