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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46A05

Retrieve articles in all journals with MSC: 46A05

Additional Information

Keywords: Nuclear spaces, (s), $ {\tilde E_V}$, product spaces, varieties, normisomorphic, Schauder basis
Article copyright: © Copyright 1972 American Mathematical Society