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Math. Proc. Camb. Phil. Soc. (2003), 134, 163 c 2003 Cambridge Philosophical Society DOI: 10.1017/S0305004102006278 Printed in the United Kingdom
 

Summary: Math. Proc. Camb. Phil. Soc. (2003), 134, 163 c 2003 Cambridge Philosophical Society
DOI: 10.1017/S0305004102006278 Printed in the United Kingdom
163
On the range of the derivatives of a smooth function between
Banach spaces
By D. AZAGRA, M. JIM ´ENEZ-SEVILLA
Departamento de An´alisis Matem´atico, Facultad de Ciencias Matem´aticas,
Universidad Complutense, 28040 Madrid, Spain.
e-mail: Daniel Azagra@mat.ucm.es, marjim@sunam1.mat.ucm.es
and R. DEVILLE
Universit´e Bordeaux I, 351, cours de la Lib´eration,
33045 Talence Cedex, France.
e-mail: deville@math.u-bordeaux.fr
(Received 5 April 2001)
Abstract
We study the size of the range of the derivatives of a smooth function between
Banach spaces. We establish conditions on a pair of Banach spaces X and Y to ensure
the existence of a Cp
smooth (Fr´echet smooth or a continuous G^ateaux smooth)
function f from X onto Y such that f vanishes outside a bounded set and all the

  

Source: Azagra Rueda, Daniel - Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid

 

Collections: Mathematics