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A remark on $ C\sb{\sigma }$ spaces


Author: Simeon Reich
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
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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... ...right\rangle \left\langle {g,p} \right\rangle \left\langle {h,p} \right\rangle $ for all $ f,g,h$ in $ E\} $.


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

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DOI: https://doi.org/10.1090/S0002-9939-1973-0326368-6
Keywords: $ {C_\sigma }$ space, extreme point
Article copyright: © Copyright 1973 American Mathematical Society

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