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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.

46G05 Derivatives of functions in infinite-dimensional spaces
47J05 Equations involving nonlinear operators (general)
Full Text: DOI
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