Abstract:The strong subdifferentiability of norms (i.e. one-sided differentiability uniform in directions) is studied in connection with some structural properties of Banach spaces. It is shown that every separable Banach space with nonseparable dual admits a norm that is nowhere strongly subdifferentiable except at the origin. On the other hand, every Banach space with a strongly subdifferentiable norm is Asplund.
Keywords: strong subdifferentiability of norms, Asplund spaces, renormings, weak compact generating
AMS Subject Classification: 46B03