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

Pérez, Ginés

doi:10.1090/S0002-9939-05-08233-X

The big slice phenomena in M-embedded and L-embedded spaces
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by Ginés López Pérez PDF

Proc. Amer. Math. Soc. 134 (2006), 273-282 Request permission

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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