Jp. Moreno, ON THE WEAK-ASTERISK MAZUR INTERSECTION PROPERTY AND FRECHET DIFFERENTIABLE NORMS ON DENSE OPEN SETS, Bulletin des sciences mathematiques, 122(2), 1998, pp. 93-105
We prove in this paper the following renorming result: every Banach sp
ace with a fundamental biorthogonal system admits an equivalent norm w
ith a dense set of locally uniformly rotund points. Then we obtain new
sufficient and necessary conditions for the existence of Frechet diff
erentiable norms and norms with the Mazur (weak Mazur) intersection p
roperty. These conditions are expressed in terms of norms which are Fr
echet differentiable on dense open sets. (C) Elsevier, Paris.