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Banach spaces having the Radon-Nikodym property and numerical index 1

Authors:	Miguel Martí n

Institution:	Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Abstract:	Let be a Banach space with the Radon-Nikodym property. Then, the following are equivalent. (i) has numerical index 1. (ii) $\vert x^{*}(x^)\vert=1$ for all $x^\in \mathrm{ex}(B_{X^})$ and $x^{}\in \mathrm{ex}(B_{X^{}})$ . (iii) is an almost-CL-space. (iv) There are a compact Hausdorff space and a linear isometry $J:X \to C(K)$ such that $\vert x^{*}(J^\delta_s)\vert=1$ for all $s\in K$ and $x^{}\in\mathrm{ex}(B_{X^{}})$ . If is a real space, the above conditions are equivalent to being semi-nicely embedded in some space .

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