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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
Posted:
June 21, 2000
MathSciNet review:
1695123
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Abstract: 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 ![$\sqrt[5]{4}$](/proc/2001-129-01/S0002-9939-00-05495-2/gif-abstract0/img4.gif) 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  .
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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:
http://dx.doi.org/10.1090/S0002-9939-00-05495-2
PII:
S 0002-9939(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
Posted:
June 21, 2000
Communicated by:
Dale Alspach
Article copyright:
© Copyright 2000 American Mathematical Society
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