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), 1901-1918

MSC (1991):
Primary 46B20, 46E40

DOI:
https://doi.org/10.1090/S0002-9947-97-01903-X

MathSciNet review:
1407701

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Abstract | References | Similar Articles | Additional Information

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 norm-one 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:
https://doi.org/10.1090/S0002-9947-97-01903-X

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