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$ M$-ideals, the strong $ 2$-ball property and some renorming theorems


Author: David Yost
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0593475-7
Article copyright: © Copyright 1981 American Mathematical Society

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