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On smooth, nonlinear surjections of Banach spaces. (English) Zbl 0898.46044
Summary: It is shown that
(1) every infinite-dimensional Banach space admits a $$C^1$$ Lipschitz map onto any separable Banach space, and
(2) if the dual of a separable Banach space $$X$$ contains a normalized, weakly null Banach-Saks sequence, then $$X$$ admits a $$C^\infty$$ map onto any separable Banach space.
Subsequently, we generalize these results to mappings onto larger target spaces.

##### MSC:
 46G05 Derivatives of functions in infinite-dimensional spaces 47J05 Equations involving nonlinear operators (general)
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##### References:
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