A classification of isomorphisms and isometries on functions spaces.

Mohammed Bachir (1)

1 Equations d'evolution

We establish in this article a formula which will allow to classify isometries as well as partial isometries between spaces of functions. Our result applies in a non compact framework and for abstract class of functions spaces included in the space of continuous and bounded functions on complete metric space. The result of this article is in particular a generalization of the Banach-Stone theorem. We use the techniques of differentiability as in the original proof of Banach for convex functions generalizing the norm of uniform convergence. We use also a duality result in a non convex framework.

Domaines: Analyse fonctionnelle [math.FA]

Mohammed Bachir. A classification of isomorphisms and isometries on functions spaces.. 2014. ⟨hal-01082632⟩