Abstract

The non-archimedean power series spaces Ap(a,t)A_p(a,t) are the most known and important examples of non-archimedean nuclear Fréchet spaces. We study when the spaces Ap(a,t)A_p(a,t) and Aq(b,s)A_q(b,s) are isometrically isomorphic. Next we determine all linear isometries on the space Ap(a,t)A_p(a,t) and show that all these maps are surjective.

Author information

Contact details are reproduced from the original publication and may be historical.

Wiesław Śliwa

Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland

sliwa@amu.edu.pl

Agnieszka Ziemkowska

Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland

aziemk@amu.edu.pl

Keywords

  • Non-archimedean power series space
  • linear isometry
  • Schauder basis

Mathematics Subject Classification

46S10, 47S10, 46A45

Suggested citation

W. Śliwa, A. Ziemkowska. “On Linear Isometries on Non-Archimedean Power Series Spaces.” Journal of Convex Analysis 19 (2012), No. 2, 453–466. https://doi.org/10.68381/jca19024

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Published by Heldermann Verlag, 2012. Rights now held by Banach Press.