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Separated sequences in nonreflexive Banach spaces


Authors: Andrzej Kryczka and Stanislaw Prus
Journal: Proc. Amer. Math. Soc. 129 (2001), 155-163
MSC (1991): Primary 46B20
DOI: https://doi.org/10.1090/S0002-9939-00-05495-2
Published electronically: June 21, 2000
MathSciNet review: 1695123
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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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Additional Information

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

Stanislaw Prus
Affiliation: Department of Mathematics, M. Curie-Skłodowska University, 20-031 Lublin, Poland
Email: bsprus@golem.umcs.lublin.pl

DOI: https://doi.org/10.1090/S0002-9939-00-05495-2
Keywords: Nonreflexive spaces, separation measure of noncompactness, James' space.
Received by editor(s): October 29, 1998
Received by editor(s) in revised form: March 14, 1999
Published electronically: June 21, 2000
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society

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