On Complemented Subspaces of Non-Archimedean Power Series Spaces

Abstract

Abstract The non-archimedean power series spaces, A1(a) and A∞(b), are the best known and most important examples of non-archimedean nuclear Fréchet spaces. We prove that the range of every continuous linear map from Ap(a) to Aq(b) has a Schauder basis if either p = 1 or p = ∞ and the set Mb,a of all bounded limit points of the double sequence (bi/aj )i, j∈ℕ is bounded. It follows that every complemented subspace of a power series space Ap(a) has a Schauder basis if either p = 1 or p = ∞ and the set Ma,a is bounded.