Norms with locally Lipschitzian derivatives |
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| Authors: | M Fabian J H M Whitfield V Zizler |
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| Institution: | (1) Sibelovia 49, 16200 Prague 6, Czechoslovakia;(2) Department of Mathematical Sciences, Lakehead University, P7B 5E1 Thunder Bay, Ontario, Canada;(3) Jihozapádní II/1084, 14100 Prague 4, Czechoslovakia |
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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. |
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