Proceedings of the American Mathematical Society

Author(s): Miguel Martín
Journal: Proc. Amer. Math. Soc. 131 (2003), 3407-3410.
MSC (2000): Primary 46B20, 47A12
Posted: June 19, 2003
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Abstract: Let

be a Banach space with the Radon-Nikodym property. Then, the following are equivalent.

(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 $x^{**}\in\mathrm{ex}(B_{X^{**}})$ .

is a real space, the above conditions are equivalent to being semi-nicely embedded in some space

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46B20, 47A12

Miguel Martín
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
Email: mmartins@ugr.es

DOI: 10.1090/S0002-9939-03-07176-4
PII: S 0002-9939(03)07176-4
Received by editor(s): November 20, 2001
Posted: June 19, 2003
Additional Notes: This research was partially supported by Spanish MCYT projects no. BFM2000-1467 and BFM2002-00061
Communicated by: Jonathan M. Borwein
Copyright of article: Copyright 2003, American Mathematical Society

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