On Linear Isometries on Strongly Regular Non-Archimedean Köthe Spaces

We study when two strongly regular Köthe spaces K(A) and K(B) are isometrically isomorphic. Next we determine all linear isometries on a strongly regular Köthe space K(A). Finally we prove that any linear isometry on a nuclear strongly regular Köthe space K(A) is surjective. The most known and important examples of nuclear strongly regular Köthe spaces are the generalized power series spaces Df(a,r).