%0 Journal Article
%A Azagra Rueda, Daniel
%A Gómez Gil, Javier
%A Fry, Robb
%A Lovo, Mauricio
%A Jaramillo Aguado, Jesús Ángel
%T C1-fine approximation of functions on Banach spaces with unconditional basis
%D 2005
%@ 0033-5606
%U https://hdl.handle.net/20.500.14352/49596
%X We show that if X is a Banach space having an unconditional basis and a Cp-smooth Lipschitz bump function, then for every C1-smooth function f from X into a Banach space Y, and for every continuous function ε : X → (0, ∞), there exists a Cp-smooth function g : X → Y such that ‖f − g‖ ≤ ε and ‖f′ − g′‖ ≤ ε.
%~