Sets of minimal points in 𝑙_{𝑝}

Lacruz, Miguel

doi:10.1090/S0002-9939-1991-1028045-6

Sets of minimal points in $l_ p$
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by Miguel Lacruz PDF

Proc. Amer. Math. Soc. 111 (1991), 139-149 Request permission

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 ${l_1}$.

References

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