Remote Access Proceedings of the American Mathematical Society
Green Open Access

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

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?)

  • [1] C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151-164. MR 22 #5872. MR 0115069 (22:5872)
  • [2] J. Diestel, Sidney A. Morris and S. Saxon, Varieties of locally convex topological vector spaces, Bull. Amer. Math. Soc. 77 (1971), 799-803. MR 0282188 (43:7901)
  • [2a] -, Varieties of linear topological spaces, Trans. Amer. Math. Soc. (to appear). MR 0316992 (47:5540)
  • [3] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. No. 16 (1955). MR 17, 763. MR 0075539 (17:763c)
  • [4] T. Kōmura and Y. Kōmura, Über die Einbettung der nuklaren Räume in $ {(s)^A}$, Math. Ann. 162 (1965/66), 284-288. MR 32 #6190. MR 0188754 (32:6190)
  • [5] H. H. Schaefer, Topological vector spaces, Macmillan, New York, 1966. MR 33 #1738. MR 0193469 (33:1689)

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

American Mathematical Society