ON THE WEAK-ASTERISK MAZUR INTERSECTION PROPERTY AND FRECHET DIFFERENTIABLE NORMS ON DENSE OPEN SETS

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.