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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 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:
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