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A smooth, non-reflexive second conjugate space

Published online by Cambridge University Press:  17 April 2009

M.A. Smith
M.A. Smith
Affiliation:
Department of Mathematics, Lake Forest College, Lake Forest, IIlinois, USA.
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Abstract

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It is shown that a separable, quasi-reflexive Banach space of deficiency one admits an equivalent norm such that its second conjugate space is smooth; this answers a question raised by Ivan Singer [Bull. Austral. Math. Soc. 12 (1975), 407–416.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 1 , August 1976 , pp. 129 - 131
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Day, Mahlon M., “Strict convexity and smoothness of normed spaces”, Trans. Amer. Math. Soc. 78 (1955), 516–528.CrossRefGoogle Scholar
[2]Day, Mahlon M., Normed linear spaces, 3rd ed. (Ergebnisse der Mathematik und ihrer Grenzgebiete, 21. Springer-Verlag, Berlin, Heidelberg, New York, 1973).CrossRefGoogle Scholar
[3]James, Robert C., “A non-reflexive Banach space isometric with its second conjugate space”, Proc. Nat. Acad. Sci. USA 37 (1951), 174–177.CrossRefGoogle ScholarPubMed
[4]Rainwater, John, “A non-reflexive Banach space has non-smooth third conjugate space”, preprint.Google Scholar
[5]Singer, Ivan, “On the problem of non-smoothness of non-reflexive second conjugate spaces”, Bull. Austral. Math. Soc. 12 (1975), 407–416.CrossRefGoogle Scholar
[6]Sullivan, Francis, Geometrical properties determined by the higher duals of a Banach space”, preprint.Google Scholar