Abstract
A short proof is given of a theorem of Lima which asserts that a Banach spaceA with the property that every family of four balls inA with the weak intersection property has a non-empty intersection, is a Lindenstrauss space, i.e.A* is isometric to anL 1(μ)-space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. Alfsen,Compact convex sets and boundary integrals, Ergebnisse Math. Grenzgebiete, Bd. 57, Springer-Verlag, Berlin and New York, 1971.
B. Hirsberg and A. Lazar,Complex Lindenstrauss spaces with extreme points, Trans. Amer. Math. Soc.186 (1973), 141–150.
O. Hustad,Intersection properties of balls in complex Banach spaces whose duals are L 1 -spaces, Acta Math.132 (1974), 283–313.
A. Lima,Complex Banach spaces whose duals are L 1 -spaces, Israel J. Math.24 (1976), 59–72.
A. Lima,An application of a theorem of Hirsberg and Lazar, Math. Scand.38 (1976), 325–340.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Roy, A.K. A short proof of a theorem on complex lindenstrauss spaces. Israel J. Math. 38, 41–45 (1981). https://doi.org/10.1007/BF02761846
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02761846