Ranges of operators and Derivatives

[EN] We show a unified method of proving the existence of C(1)-Frechet 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 omega(1). (C) 2009 Elsevier Inc. All rights reserved.Research supported by Project MTM2008-05396 and the Universidad Politecnica de Valencia. Research supported by the grants A100190502, IAA 100190801 and Inst. Research Plan AV0Z10190503. Research supported by Project MTM2008-03211 and the Universidad Politecnica de Valencia.Guirao Sánchez, AJ.; Hájek, P.; Montesinos Santalucia, V. (2010). Ranges of operators and Derivatives. Journal of Mathematical Analysis and Applications. 367(1):29-33. https://doi.org/10.1016/j.jmaa.2009.12.0102933367