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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Embedding nuclear spaces in products of an arbitrary Banach space


Author: Stephen A. Saxon
Journal: Proc. Amer. Math. Soc. 34 (1972), 138-140
MSC: Primary 46A05
MathSciNet review: 0318823
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Abstract: It is proved that if E is an arbitrary nuclear space and F is an arbitrary infinite-dimensional Banach space, then there exists a fundamental (basic) system $ \mathcal{V}$ of balanced, convex neighborhoods of zero for E such that, for each V in $ \mathcal{V}$, the normed space $ {E_V}$ is isomorphic to a subspace of F. The result for $ F = {l_p}\;(1 \leqq p \leqq \infty )$ was proved by A. Grothendieck.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0318823-9
PII: S 0002-9939(1972)0318823-9
Keywords: Nuclear spaces, (s), $ {\tilde E_V}$, product spaces, varieties, normisomorphic, Schauder basis
Article copyright: © Copyright 1972 American Mathematical Society