Proceedings of the American Mathematical Society

Author(s): Andrzej Kryczka; Stanislaw Prus
Journal: Proc. Amer. Math. Soc. 129 (2001), 155-163.
MSC (1991): Primary 46B20
Posted: June 21, 2000
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We prove that there is

such that the unit ball of any nonreflexive Banach space contains a

-separated sequence. The supremum of these constants

is estimated from below by $\sqrt[5]{4}$ and from above approximately by

. Given any

, 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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Andrzej Kryczka
Affiliation: Department of Mathematics, M. Curie-Sklodowska University, 20-031 Lublin, Poland
Email: akryczka@golem.umcs.lublin.pl

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