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Differentiable functions and rough norms on Banach spaces. (English) Zbl 0236.46051

MSC:
46B99 Normed linear spaces and Banach spaces; Banach lattices
46G05 Derivatives of functions in infinite-dimensional spaces
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
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[1] Robert Bonic and John Frampton, Differentiable functions on certain Banach spaces, Bull. Amer. Math. Soc. 71 (1965), 393 – 395. · Zbl 0131.12905
[2] M. Ĭ. Kadec\(^{\prime}\), Conditions for the differentiability of a norm in a Banach space, Uspehi Mat. Nauk 20 (1965), no. 3 (123), 183 – 187 (Russian).
[3] J. Kurzweil, On approximation in real Banach spaces, Studia Math. 14 (1954), 214 – 231 (1955). · Zbl 0064.10802
[4] Guillermo Restrepo, Differentiable norms in Banach spaces, Bull. Amer. Math. Soc. 70 (1964), 413 – 414. · Zbl 0173.41304
[5] Guillermo Restrepo, Differentiable norms, Bol. Soc. Mat. Mexicana (2) 10 (1965), 47 – 55. · Zbl 0173.15603
[6] J. H. M. Whitfield, Differentiable functions with bounded nonempty support on Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 145 – 146. · Zbl 0134.32404
[7] Michel Leduc, Densité de certaines familles d’hyperplans tangents, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A326 – A328 (French). · Zbl 0193.10801
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