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)

 

Sets of minimal points in $ l\sb p$


Author: Miguel Lacruz
Journal: Proc. Amer. Math. Soc. 111 (1991), 139-149
MSC: Primary 46B20
MathSciNet review: 1028045
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that the minimal hull of a convex set in a Banach space is not necessarily convex, even in $ {l_p}$ spaces (finite- or infinite-dimensional). This answers a question raised by B. Beauzamy and B. Maurey in their joint paper of 1977. We also carry out a careful study of the minimal hull and the saturation of the unit ball in $ l_1^{(N)}$. Finally, we give a compactness theorem for the minimal hull in $ {l_1}$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B20

Retrieve articles in all journals with MSC: 46B20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1028045-6
PII: S 0002-9939(1991)1028045-6
Keywords: Convex set, minimal hull, compact set
Article copyright: © Copyright 1991 American Mathematical Society