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.
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This author's research supported in part by NSERC (Canada) Grant A7535.
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Fabian, M., Whitfield, J.H.M. & Zizler, V. Norms with locally Lipschitzian derivatives. Israel J. Math. 44, 262–276 (1983). https://doi.org/10.1007/BF02760975
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DOI: https://doi.org/10.1007/BF02760975