Nondentable solid subsets in Banach lattices failing RNP. Applications to renormings
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- by Elisabeth Werner PDF
- Proc. Amer. Math. Soc. 107 (1989), 611-620 Request permission
Abstract:
We show that for every Banach lattice $E$ failing RNP and not containing ${c_0}$ (resp. containing ${c_0}$) and for every $\varepsilon > 0$ there exists a solid convex closed subset $D$ of the unit ball of $E$, such that \[ \operatorname {dist} [\operatorname {ext} ({\overline D ^{\sigma ({E^{ * * }},{E^ * })}}),E] > 1 - \varepsilon (\operatorname {resp} . > \tfrac {1}{2} - \varepsilon )\] and such that every slice of $D$ has diameter bigger than $2 - \varepsilon$. We also prove that these results are optimal. We apply them to construct rough lattice norms with almost optimal constant on non-Asplund Banach lattices.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 611-620
- MSC: Primary 46B30; Secondary 46B22
- DOI: https://doi.org/10.1090/S0002-9939-1989-1017225-2
- MathSciNet review: 1017225