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Journal of Convex Analysis 26 (2019), No. 1, 325--340
Copyright Heldermann Verlag 2019

On Linear Isometries on Strongly Regular Non-Archimedean Köthe Spaces

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

Agnieszka Ziemkowska
Institute of Mathematics, Poznan University of Technology, ul. Piotrowo 3A, 60-965 Poznan, Poland

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).

Keywords: Non-Archimedean Köthe spaces, isometrical isomorphy, Schauder basis.

MSC: 46S10, 47S10, 46A35

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