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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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Keywords: Nuclear spaces, (<I>s</I>), <!– MATH ${\tilde E_V}$ –> <IMG WIDTH="34" HEIGHT="48" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${\tilde E_V}$">, product spaces, varieties, normisomorphic, Schauder basis
Article copyright: © Copyright 1972 American Mathematical Society