Journal of Convex Analysis 19 (2012), No. 2, 453--466
Copyright Heldermann Verlag 2012
On Linear Isometries on Non-Archimedean Power Series Spaces
Wieslaw Sliwa
Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61-614 Poznan, Poland
sliwa@amu.edu.pl
Agnieszka Ziemkowska
Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61-614 Poznan, Poland
aziemk@amu.edu.pl
The non-archimedean power series spaces Ap(a,t) are the most known and important examples of non-archimedean nuclear Fréchet spaces. We study when the spaces Ap(a,t) and Aq(b,s) are isometrically isomorphic. Next we determine all linear isometries on the space Ap(a,t) and show that all these maps are surjective.
Keywords: Non-archimedean power series space, linear isometry, Schauder basis.
MSC: 46S10, 47S10, 46A45
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