Separated sequences in nonreflexive Banach spaces

Kryczka, Andrzej; Prus, Stanisław

doi:10.1090/S0002-9939-00-05495-2

Separated sequences in nonreflexive Banach spaces
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by Andrzej Kryczka and Stanisław Prus PDF

Proc. Amer. Math. Soc. 129 (2001), 155-163 Request permission

Abstract:

We prove that there is $c>1$ such that the unit ball of any nonreflexive Banach space contains a $c$-separated sequence. The supremum of these constants $c$ is estimated from below by $\sqrt [5]{4}$ and from above approximately by $1.71$. Given any $p>1$, we also construct a nonreflexive space so that if the convex hull of a sequence is sufficiently close to the unit sphere, then its separation constant does not exceed $2^{1/p}$.

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