We show that every infinite-dimensional Banach space with separable dual admits an equivalent norm which is weakly locally uniformly rotund but not locally uniformly rotund.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-2-8, author = {Szymon Draga}, title = {On weakly locally uniformly rotund norms which are not locally uniformly rotund}, journal = {Colloquium Mathematicae}, volume = {139}, year = {2015}, pages = {241-246}, zbl = {1332.46009}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-2-8} }
Szymon Draga. On weakly locally uniformly rotund norms which are not locally uniformly rotund. Colloquium Mathematicae, Tome 139 (2015) pp. 241-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-2-8/