CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

On the Composition of Differentiable Functions

  Published:2003-12-01
 Printed: Dec 2003
  • M. Bachir
  • G. Lancien
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

We prove that a Banach space $X$ has the Schur property if and only if every $X$-valued weakly differentiable function is Fr\'echet differentiable. We give a general result on the Fr\'echet differentiability of $f\circ T$, where $f$ is a Lipschitz function and $T$ is a compact linear operator. Finally we study, using in particular a smooth variational principle, the differentiability of the semi norm $\Vert \ \Vert_{\lip}$ on various spaces of Lipschitz functions.
MSC Classifications: 58C20, 46B20 show english descriptions Differentiation theory (Gateaux, Frechet, etc.) [See also 26Exx, 46G05]
Geometry and structure of normed linear spaces
58C20 - Differentiation theory (Gateaux, Frechet, etc.) [See also 26Exx, 46G05]
46B20 - Geometry and structure of normed linear spaces
 

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/