Isomorphisms with small bound between spaces of p-adic continuous functions

JESÚS ARAUJO

Abstract:

In the real setting, the Banach-Stone theorem says that given two compact spaces X and Y, the existence of an isometry between C(X) and C(Y) (endowed with the sup norm) implies that X and Y are homeomorphic. It is also known that, in the same context, a similar result can be obtained if there exists a linear isomorphism $T: C(X) \rightarrow C(Y)$ satisfying $\Vert T \Vert \cdot \Vert T^{-1} \Vert <2$.

Here we deal with isomorphims between spaces of p-adic valued functions endowed with an A-norm, and study when a homeomorphism between topological spaces can be obtained.