An extension of the Banach-Stone theorem

Mohammed Bachir (1)

1 Equations d'evolution

We establish an extension of the Banach-Stone theorem to a class of isomorphism more general than isometries in a non compact framework. Some applications are given. In particular, we give a canonical representations of some (not necessarily linear) operators between product of function spaces. Our results are established for abstract class of function spaces included in the space of all continuous and bounded functions defined on a complete metric space.

Domaines: Analyse fonctionnelle [math.FA]

Mohammed Bachir. An extension of the Banach-Stone theorem. Journal of the Australian Mathematical Society, 2018, 105 (1), pp.1-23. ⟨hal-01552157⟩