Weakly Locally Uniformly Rotund Norm which is not Locally Uniformly Rotund

The aim of this paper is to provide a proof of the fact that a weakly locally uniformly rotund norm does not have to be locally uniformly rotund. This result is well-known for experts in Geometry of Banach Spaces. However, since the justification of this result is omitted in the literature, we believe that the present note may be helpful for students or novices in the theory.

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