Extreme points and $l_{1}(\Gamma )$-spaces
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- by Nina M. Roy PDF
- Proc. Amer. Math. Soc. 86 (1982), 216-218 Request permission
Abstract:
Let $X$ be a nontrivial real Banach space and let ${E_X}$ denote the set of extreme points of the closed unit ball $B(X)$. Theorem 1. $X$ is an ${l_1}(\Gamma )$-space if and only if (i) ${\text {span}}(e)$ is an $L$-summand in $X$ for every $e$ in ${E_X}$ and (ii) $B(X)$ is the norm closed convex hull of ${E_X}$. Theorem 2. Let $X = {Y^ * }$. If (i) ${\text {span}}(e)$ is an $L$-summand in $X$ for every $e$ in ${E_X}$ and (ii) $\left \{ {e \in {E_X}:e(y) = 1} \right \}$ is countable for each $y$ in $Y$ with $\left \| y \right \| = 1$, then $X$ is an ${l_1}(\Gamma )$-space.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 216-218
- MSC: Primary 46B25; Secondary 46E30
- DOI: https://doi.org/10.1090/S0002-9939-1982-0667277-8
- MathSciNet review: 667277