Embedding nuclear spaces in products of an arbitrary Banach space

Saxon, Stephen A.

doi:10.1090/S0002-9939-1972-0318823-9

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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