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Criteria for convexity in Banach spaces


Author: Vassilis Kanellopoulos
Journal: Proc. Amer. Math. Soc. 128 (2000), 2725-2733
MSC (2000): Primary 52A07, 46B20; Secondary 46B22
DOI: https://doi.org/10.1090/S0002-9939-00-05300-4
Published electronically: February 28, 2000
MathSciNet review: 1662253
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Abstract:

In this paper two convexity criteria are proven. The first one characterizes compact convex sets in a locally convex space and extends a previous result by G. Aumann, while the second one characterizes closed bounded convex sets with the Radon-Nikodým property in a Banach space.


References [Enhancements On Off] (What's this?)

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Additional Information

Vassilis Kanellopoulos
Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis 15784, Athens, Greece
Email: bkanel@math.uoa.gr

DOI: https://doi.org/10.1090/S0002-9939-00-05300-4
Keywords: Convex set, locally convex space, Banach space, extreme point, slice, contractible set, Radon-Nikod\'{y}m property
Received by editor(s): October 6, 1997
Received by editor(s) in revised form: October 6, 1998
Published electronically: February 28, 2000
Additional Notes: This research was financially supported by I.K.Y. (National Foundation for Scholarships)
Communicated by: Dale E. Alspach
Article copyright: © Copyright 2000 American Mathematical Society

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