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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Extreme points of unit balls
in Lipschitz function spaces


Author: Ryszard Smarzewski
Journal: Proc. Amer. Math. Soc. 125 (1997), 1391-1397
MSC (1991): Primary 46B20
MathSciNet review: 1389537
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Abstract: We give a new characterization of the set $\mathop {\rm ext}\left ( B_{X^{\#}}\right ) $ of all extreme points of the unit ball $B_{X^{\#}}$ in the Banach space $X^{\#}$ of all Lipschitz functions on a metric space $X.$ This result is applied to get a total variation characterization of $\mathop {\rm ext}\left ( B_{X^{\#}}\right )$ in the particular case when $X$ is a convex subset of a Banach space.


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Additional Information

Ryszard Smarzewski
Affiliation: Department of Mathematics, M. Curie-Sklodowska University, 20-031 Lublin, Poland
Address at time of publication: Institute of Mathematics, Catholic University of Lublin, Al. Raclawickie 14, 20-950 Lublin, Poland
Email: smarz@golem.umcs.lublin.pl

DOI: https://doi.org/10.1090/S0002-9939-97-03866-5
Keywords: Lipschitz functions, extreme points, total variation characterization.
Received by editor(s): November 13, 1995
Communicated by: Dale Alspach
Article copyright: © Copyright 1997 American Mathematical Society