Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: February 28, 2000
MathSciNet review: 1662253
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 52A07, 46B20, 46B22

Retrieve articles in all journals with MSC (2000): 52A07, 46B20, 46B22


Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05300-4
PII: S 0002-9939(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