On tame operators between non-archimedean power series spaces

Let p . {1,.}. We show that any continuous linear operator T from A 1(a) to A p (b) is tame, i.e., there exists a positive integer c such that sup x .T x . k /|x| ck < . for every k . .. Next we prove that a similar result holds for operators from A .(a) to A p (b) if and only if the set M b,a of all finite limit points of the double sequence (b i /a j )i,j.. is bounded. Finally we show that the range of every tame operator from A .(a) to A .(b) has a Schauder basis.