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

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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

References

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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 LLC.