A remark on $C_{\sigma }$ spaces
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- by Simeon Reich PDF
- Proc. Amer. Math. Soc. 40 (1973), 215-216 Request permission
Abstract:
We give a simple new proof of the following result, conjectured by Effros and proved by Fakhoury: Let $E$ be a ${C_\sigma }$ space and $Z$ the set of extreme points of the unit ball of ${E^ \ast }$. Then $Z \cup \{ 0\} = \{ p \in {E^ \ast }:\left \langle {fgh,p} \right \rangle = \left \langle {f,p} \right \rangle \left \langle {g,p} \right \rangle \left \langle {h,p} \right \rangle$ for all $f,g,h$ in $E\}$.References
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M. M. Day, Normed linear spaces, 2nd rev. ed., Academic Press, New York; Springer-Verlag, Berlin, 1962. MR 26 #2847.
- Edward G. Effros, On a class of real Banach spaces, Israel J. Math. 9 (1971), 430–458. MR 296658, DOI 10.1007/BF02771459
- Hicham Fakhoury, Préduaux de $L$-espaces et éléments extrémaux, C. R. Acad. Sci. Paris Sér. A-B 272 (1971), A1703–A1706 (French). MR 280981 —, Préduaux de $L$-espaces: notion de centre, J. Functional Analysis 9 (1972), 189-207.
- M. Sharir, Extremal structure in operator spaces, Trans. Amer. Math. Soc. 186 (1973), 91–111. MR 333829, DOI 10.1090/S0002-9947-1973-0333829-7
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 215-216
- MSC: Primary 46E15
- DOI: https://doi.org/10.1090/S0002-9939-1973-0326368-6
- MathSciNet review: 0326368