On linear isometries on non-archimedean powerseries spaces

Abstract

The non-archimedean power series spaces Ap(a; t) are the most known and important examples of non-archimedean nuclear Frechet spaces. We study when the spaces Ap(a; t) and Aq(b; s) are isometrically isomorphic. Next we determine all linear isometries on the space Ap(a; t) and show that all these maps are surjective.