Some generalizations of locally uniform rotundity
The authors introduce and study some generalizations of locally uniformly rotund (LUR) norms -- ALUR and WALUR norms. Some characterizations of pointwise versions of these notions are given. Existence of a WALUR norm implies \(\sigma\)-fragmentability of the space but it is not known whether it implies LUR renormability (cf. Question 2 in the paper).
weakly almost locally uniformly rotund norm
scientific article; zbMATH DE number 1563099