On smooth, nonlinear surjections of banach spaces
Tóm tắt
It is shown that (1) every infinite-dimensional Banach space admits aC
1 Lipschitz map onto any separable Banach space, and (2) if the dual of a separable Banach spaceX contains a normalized, weakly null Banach-Saks sequence, thenX admits aC
∞ map onto any separable Banach space. Subsequently, we generalize these results to mappings onto larger target spaces.
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