Disappearance of extreme points

Morris, Peter

doi:10.1090/S0002-9939-1983-0695251-5

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Disappearance of extreme points
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Proc. Amer. Math. Soc. 88 (1983), 244-246 Request permission

Abstract:

It is shown that every separable Banach space which contains an isomorphic copy of ${c_0}$ is isomorphic to a strictly convex space $E$ such that no point of $E$ is an extreme point of the unit ball of ${E^{ * * }}$.

References

J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964
R. R. Phelps, Extreme points of polar convex sets, Proc. Amer. Math. Soc. 12 (1961), 291–296. MR 121634, DOI 10.1090/S0002-9939-1961-0121634-3