On the extremal structure of the unit balls of Banach spaces of weakly continuous functions and their duals
Authors:
Zhibao Hu and Mark A. Smith
Journal:
Trans. Amer. Math. Soc. 349 (1997), 19011918
MSC (1991):
Primary 46B20, 46E40
MathSciNet review:
1407701
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Abstract: A sufficient and then a necessary condition are given for a function to be an extreme point of the unit ball of the Banach space of continuous functions, under the supremum norm, from a compact Hausdorff topological space into a Banach space equipped with its weak topology . Strongly extreme points of the unit ball of are characterized as the normone functions that are uniformly strongly extreme point valued on a dense subset of . It is shown that a variety of stronger types of extreme points (e.g. denting points) never exist in the unit ball of . Lastly, some naturally arising and previously known extreme points of the unit ball of are shown to actually be strongly exposed points.
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Additional Information
Zhibao Hu
Affiliation:
Division of Mathematics, El Paso Community College, Valle Verde Campus, P.O. Box 20500, El Paso, Texas 79998
Mark A. Smith
Affiliation:
Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056
DOI:
http://dx.doi.org/10.1090/S000299479701903X
PII:
S 00029947(97)01903X
Keywords:
Extreme points,
strongly extreme points,
points of continuity,
denting points,
spaces of weakly continuous functions
Received by editor(s):
November 9, 1995
Additional Notes:
The second author was supported in part by a Miami University Summer Research Grant.
Article copyright:
© Copyright 1997
American Mathematical Society
