On Linear Isometries on Non-Archimedean Power Series Spaces

The non-archimedean power series spaces

are the most known and important examples of non-archimedean nuclear Fréchet spaces. We study when the spaces

A_p(a,t) A p ( a , t )

and

A_q(b,s) A q ( b , s )

are isometrically isomorphic. Next we determine all linear isometries on the space

A_p(a,t) A p ( a , t )

and show that all these maps are surjective.