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Nuclearity and Banach spaces

Published online by Cambridge University Press:  20 January 2009

Manuel Valdivia
Manuel Valdivia
Affiliation:
Facultad de Ciencias, Paseo al Mar, 13, Valencia (Espana)
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Summary

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Let E be a nuclear space provided with a topology different from the weak topology. Let {Ai: i ∈ I} be a fundamental system of equicontinuous subsets of the topological dual E' of E. If {Fi: i ∈ I} is a family of infinite dimensional Banach spaces with separable predual, there is a fundamental system {Bi: i ∈ I} of weakly closed absolutely convex equicontinuous subsets of E'such that is norm-isomorphic to Fi, for each i ∈ I. Other results related with the one above are also given.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 20 , Issue 3 , March 1977 , pp. 205 - 209
Copyright
Copyright © Edinburgh Mathematical Society 1977

References

REFERENCE

(1) Grothendieck, A., Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).Google Scholar
(2) Jarchow, H., lp-characterizations of nuclear locally convex spaces (To be published).Google Scholar
(3) Ovsepian, R. I. and Pelczynski, A., The existence in every separable Banach space of a fundamental total and bounded bi-orthogonal sequence and related constructions of uniformly bounded orthonormal systems in L2 (Seminaire Maurey-Schwartz, Paris, 1973–1974).Google Scholar
(4) Pietsch, A., Nuclear locally convex spaces (Berlin-Heidelberg-New York, Springer, 1972).Google Scholar
(5) Saxon, S. A., Embedding nuclear spaces in products of an arbitrary Banach space, Proc. Amer. Math. Soc. 34 (1972), 138–140.Google Scholar