Geodesic
Locally Uniformly Rotund Renorming and Injections Into c0(Γ)
Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 494-500

Voir la notice de l'article provenant de la source Cambridge University Press

A norm |⋅| on a Banach space X is locally uniformly rotund (LUR) if lim |x n — x| = 0 for every x n , x ∈ X for which lim2|x|2 + 2 |x n |2-|xn+x n|2 = 0. It is shown that a Banach space X admits an equivalent LUR norm provided there is a bounded linear operator T of X into c0(Γ) such that T* c*0(Γ) is norm dense in X*. This is the case e.g. if X* is weakly compactly generated (WCG).
DOI : 10.4153/CMB-1984-079-8
Mots-clés : 46, B 20, renorming, local uniform rotundity, differentiability of the norm 
Godefroy, G.; Troyanski, S.; Whitfield, J.; Zizler, V. Locally Uniformly Rotund Renorming and Injections Into c0(Γ). Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 494-500. doi: 10.4153/CMB-1984-079-8
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