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On uniformly Gâteaux smooth C ( n ) -smooth norms on separable Banach spaces

Marián J. Fabián, Václav Zizler (1999)

Czechoslovak Mathematical Journal

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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.