Geodesic
On Uniformly Convex and Uniformly Kadec-Klee Renomings
Serdica Mathematical Journal, Tome 21 (1995) no. 1, pp. 1-18

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We give a new construction of uniformly convex norms with a power type modulus on super-reflexive spaces based on the notion of dentability index. Furthermore, we prove that if the Szlenk index of a Banach space is less than or equal to ω (first infinite ordinal) then there is an equivalent weak* lower semicontinuous positively homogeneous functional on X* satisfying the uniform Kadec-Klee Property for the weak*-topology (UKK*). Then we solve the UKK or UKK* renorming problems for Lp(X) spaces and C(K) spaces for K scattered compact space.
Keywords: Renorming, Szlenk Index, Dentability, Uniformly Convex, Kadec-Klee, Super-Reflexive, Scattered Compact, Lp Spaces 
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     author = {Lancien, Gilles},
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Lancien, Gilles. On Uniformly Convex and Uniformly Kadec-Klee Renomings. Serdica Mathematical Journal, Tome 21 (1995) no. 1, pp. 1-18. http://geodesic.mathdoc.fr/item/SMJ2_1995_21_1_a0/