Abstract
For a family of closed balls in a normed space we define the concept of weak intersection property, and we show that a complex Banch space is a
space if and only if every family of closed balls with the weak intersection property has a non-empty intersection.
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References
O. Hustad,Intersection properties of balls in complex Banach spaces whose duals are L 1 spaces, Preprint Series, Inst. Math., University of Oslo, No. 9, (1973).
J. Lindenstrauss,Extension of compact operators, Mem. Amer. Math. Soc.48 (1964).
L. Nachbin,A theorem of the Hahn-Banach type for linear transformations, Trans. Amer. Math. Soc.68 (1950), 28–46.
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Hustad, O. A note on complex
spaces.
Israel J. Math. 16, 117–119 (1973). https://doi.org/10.1007/BF02761976
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DOI: https://doi.org/10.1007/BF02761976