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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Sets of minimal points in $ l\sb p$

Author: Miguel Lacruz
Journal: Proc. Amer. Math. Soc. 111 (1991), 139-149
MSC: Primary 46B20
MathSciNet review: 1028045
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Abstract: We show that the minimal hull of a convex set in a Banach space is not necessarily convex, even in $ {l_p}$ spaces (finite- or infinite-dimensional). This answers a question raised by B. Beauzamy and B. Maurey in their joint paper of 1977. We also carry out a careful study of the minimal hull and the saturation of the unit ball in $ l_1^{(N)}$. Finally, we give a compactness theorem for the minimal hull in $ {l_1}$.

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PII: S 0002-9939(1991)1028045-6
Keywords: Convex set, minimal hull, compact set
Article copyright: © Copyright 1991 American Mathematical Society