Abstract view
On Complemented Subspaces of NonArchimedean Power Series Spaces


Published:20110308
Printed: Oct 2011
Wiesław Śliwa,
Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61614 Poznań, Poland
Agnieszka Ziemkowska,
Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61614 Poznań, Poland
Abstract
The nonarchimedean power series spaces, $A_1(a)$ and $A_\infty(b)$, are the
best known and most important examples of nonarchimedean nuclear Fréchet 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.