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Ranges of operators and derivatives

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
367
Issue
1
Identifiers
DOI: 10.1016/j.jmaa.2009.12.010
Keywords
  • Fréchet Smoothness
  • Surjective Mappings

Abstract

Abstract We show a unified method of proving the existence of C 1 -Fréchet smooth and Lipschitz mappings which are surjective or whose range of the derivative contains the whole dual unit ball. As an application, under Martin's Maximum axiom, we obtain a complete result for those spaces with density character ω 1 .

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