, Volume 44, Issue 3, pp 262-276

Norms with locally Lipschitzian derivatives

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Abstract

If a separable Banach spaceX admits a real valued function ф with bounded nonempty support, φ 艂 is locally Lipschitzian and if no subspace ofX is isomorphic toc o, thenX admits an equivalent twice Gateaux differentiable norm whose first Frechet differential is Lipschitzian on the unit sphere ofX.

This author's research supported in part by NSERC (Canada) Grant A7535.