$M$-ideals, the strong $2$-ball property and some renorming theorems
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- by David Yost PDF
- Proc. Amer. Math. Soc. 81 (1981), 299-303 Request permission
Abstract:
Examples are given of $M$-ideals in Banach spaces which do not possess the strong $2$-ball property. This solves a problem of Alfsen and Effros. A previous example is shown to be incorrect. The technique used to construct these examples is then employed to prove negative renorming theorems for Banach spaces. The following is representative: every separable Banach space has an equivalent norm which is strictly convex but not locally uniformly convex.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 299-303
- MSC: Primary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-1981-0593475-7
- MathSciNet review: 593475