Geodesic
Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis
Serdica Mathematical Journal, Tome 26 (2000) no. 4, pp. 353-358

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It is shown that a Banach space X admits an equivalent uniformly Gateaux differentiable norm if it has an unconditional basis and X* admits an equivalent norm which is uniformly rotund in every direction.
Keywords: Unconditional Basis, Uniformly Gateaux Smooth Norms, Uniform Eberlein Compacts, Uniform Rotundity In Every Direction 
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     author = {Rychter, Jan},
     title = {Uniformly {G\^ateaux} {Differentiable} {Norms} in {Spaces} with {Unconditional} {Basis}},
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Rychter, Jan. Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis. Serdica Mathematical Journal, Tome 26 (2000) no. 4, pp. 353-358. http://geodesic.mathdoc.fr/item/SMJ2_2000_26_4_a4/