Geodesic
On uniformly Gâteaux smooth $C^{(n)}$-smooth norms on separable Banach spaces
Czechoslovak Mathematical Journal, Tome 49 (1999) no. 3, pp. 657-672 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Every separable Banach space with $C^{(n)}$-smooth norm (Lipschitz bump function) admits an equivalent norm (a Lipschitz bump function) which is both uniformly Gâteaux smooth and $C^{(n)}$-smooth. If a Banach space admits a uniformly Gâteaux smooth bump function, then it admits an equivalent uniformly Gâteaux smooth norm.
Every separable Banach space with $C^{(n)}$-smooth norm (Lipschitz bump function) admits an equivalent norm (a Lipschitz bump function) which is both uniformly Gâteaux smooth and $C^{(n)}$-smooth. If a Banach space admits a uniformly Gâteaux smooth bump function, then it admits an equivalent uniformly Gâteaux smooth norm.
Classification : 46B03, 46B20 
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     author = {Fabian, Mari\'an and Zizler, V\'aclav},
     title = {On uniformly {G\^ateaux} smooth $C^{(n)}$-smooth norms on separable {Banach} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {657--672},
     year = {1999},
     volume = {49},
     number = {3},
     mrnumber = {1708330},
     zbl = {1011.46010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_1999_49_3_a15/}
}
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Fabian, Marián; Zizler, Václav. On uniformly Gâteaux smooth $C^{(n)}$-smooth norms on separable Banach spaces. Czechoslovak Mathematical Journal, Tome 49 (1999) no. 3, pp. 657-672. http://geodesic.mathdoc.fr/item/CMJ_1999_49_3_a15/

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