Bidual renormings of Banach spaces
2009 - S. Lajara, A. J. Pallares, S. Troyanski
Journal of Mathematical Analysis and Applications 350, 630-639 (2009).
authors IMACI
Abtract
Given a separable Banach space X with no isomorphic copies of l(1) and a separable subspace Y of its bidual, we provide a Sufficient condition on Y to ensure that X admits an equivalent norm such that the restriction to Y of the Corresponding bidual norm is midpoint locally uniformly rotund. This result applies to the separable subspaces of the bidual of a Banach space with a shrinking unconditional Schauder basis and to the bidual of the James space.