On tame operators between non-archimedean power seris spaces

Abstract

Let p {1∞}. We show that any continuous linear operator T from A1(a) to Ap(b) is tame i.e. there exists a positive integer c such that supx IITxIIk=/IxIck < ∞ for every k N. Next we prove that a similar result holds for operators from A∞(a) to Ap(b) if and only if the set Mba of all finite limit points of the double sequence (bj/ai/I,j N is bounded. Finally we show that the range of every tame operator from A∞(a) to A∞(b) has a Schauder basis.