On some renorming problems. II
Competing results from an earlier paper [part I, Arch. Math. 48, 505-510 (1987; Zbl 0629.46030)] the author proves: Every Banach function lattice X over a positive \(\sigma\)-finite measure space admits an equivalent norm that is uniformly rotund in every direction. If additionally, X is reflexive, and \(\mu\) is separable, then X admits an equivalent norm which is simultaneously uniformly rotund in every direction and weakly uniformly rotund.
equivalent norm that is uniformly rotund in every direction
scientific article; zbMATH DE number 4144727