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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Embedding nuclear spaces in products of an arbitrary Banach space
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by Stephen A. Saxon PDF
Proc. Amer. Math. Soc. 34 (1972), 138-140 Request permission

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
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 138-140
  • MSC: Primary 46A05
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0318823-9
  • MathSciNet review: 0318823