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The big slice phenomena in M-embedded and L-embedded spaces


Author: Ginés López Pérez
Journal: Proc. Amer. Math. Soc. 134 (2006), 273-282
MSC (2000): Primary 46B20, 46B22
DOI: https://doi.org/10.1090/S0002-9939-05-08233-X
Published electronically: August 15, 2005
MathSciNet review: 2170568
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Abstract: We obtain sufficient conditions on an M-embedded or L-embedded space so that every nonempty relatively weakly open subset of its unit ball has norm diameter 2. We prove that, up to renorming, this holds for every Banach space containing $c_0$ and, as a consequence, for every proper M-ideal. The result obtained for L-embedded spaces can be applied to show that the above property is satisfied for every predual of an atomless real JBW*-triple. As a consequence, a characterization of the Radon-Nikodym property is obtained in this setting, showing that a predual of a real JBW*-triple E verifies the Radon-Nikodym property if, and only if, E is the $l_{\infty}$-sum of real type I triple factors.


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Additional Information

Ginés López Pérez
Affiliation: Facultad de Ciencias, Departamento de Análisis Matemático, Universidad de Gra- nada, 18071-Granada, Spain
Email: glopezp@ugr.es

DOI: https://doi.org/10.1090/S0002-9939-05-08233-X
Keywords: Denting point, slices, weakopen subsets
Received by editor(s): September 8, 2004
Published electronically: August 15, 2005
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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