Every non-reflexive Banach space admits an equivalent norm with a unit sphere point that is strongly exposed by all supporting functionals but not almost locally uniformly rotund, while the 2004 characterization holds in reflexive spaces.
Draga, On weakly locally uniformly rotund norms which are not local ly uniformly rotund , Coll
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Some remarks on almost locally uniformly rotund points
Every non-reflexive Banach space admits an equivalent norm with a unit sphere point that is strongly exposed by all supporting functionals but not almost locally uniformly rotund, while the 2004 characterization holds in reflexive spaces.