Search: MSC category 47S10 ( Operator theory over fields other than ${\bf R}$, ${\bf C}$ or the quaternions; non-Archimedean operator theory )
 On Complemented Subspaces of Non-Archimedean Power Series Spaces The non-archimedean power series spaces, $A_1(a)$ and $A_\infty(b)$, are the best known and most important examples of non-archimedean nuclear FrÃ©chet spaces. We prove that the range of every continuous linear map from $A_p(a)$ to $A_q(b)$ has a Schauder basis if either $p=1$ or $p=\infty$ and the set $M_{b,a}$ of all bounded limit points of the double sequence $(b_i/a_j)_{i,j\in\mathbb{N}}$ is bounded. It follows that every complemented subspace of a power series space $A_p(a)$ has a Schauder basis if either $p=1$ or $p=\infty$ and the set $M_{a,a}$ is bounded. Keywords:non-archimedean KÃ¶the space, range of a continuous linear map, Schauder basisCategories:46S10, 47S10, 46A35