On Frechet norms and Mazur's Intersection Property

Jan Rychtář

Charles University, Prague; University of North Carolina at Greensboro

We show that a Banach space admits an equivalent norm with Mazur's intersection property if it contains a subspace having (1) a Frechet smooth norm and (2) a dual with the full weak* density. In the proof we will extensively use biorthogonal systems and results of M. Jimenez Sevilla and J. P. Moreno on spaces with Mazur's interesction property.