Abstract

We study when two strongly regular Köthe spaces K(A) and K(B) are isometrically isomorphic. Next we determine all linear isometries on a strongly regular Köthe space K(A). Finally we prove that any linear isometry on a nuclear strongly regular Köthe space K(A) is surjective. The most known and important examples of nuclear strongly regular Köthe spaces are the generalized power series spaces Df(a,r)D_f(a,r).

Author information

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

Wiesław Śliwa

Faculty of Mathematics and Natural Sciences, University of Rzeszów, ul. Pigonia 1, 35-310 Rzeszów, Poland

wsliwa@ur.edu.pl

Keywords

  • Non-Archimedean Köthe spaces
  • isometrical isomorphy
  • Schauder basis

Mathematics Subject Classification

46S10, 47S10, 46A35

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Suggested citation

W. Śliwa, A. Ziemkowska. “On Linear Isometries on Strongly Regular Non-Archimedean Köthe Spaces.” Journal of Convex Analysis 26 (2019), No. 1, 325–340. https://doi.org/10.68381/jca26018

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press LLC.