
Journal of Convex Analysis 26 (2019), No. 1, 325340 Copyright Heldermann Verlag 2019 On Linear Isometries on Strongly Regular NonArchimedean Köthe Spaces Wieslaw Sliwa Faculty of Mathematics and Natural Sciences, University of Rzeszow, ul. Pigonia 1, 35310 Rzeszow, Poland wsliwa@ur.edu.pl Agnieszka Ziemkowska Institute of Mathematics, Poznan University of Technology, ul. Piotrowo 3A, 60965 Poznan, Poland agnieszka.ziemkowska@put.poznan.pl 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 D_{f}(a,r). Keywords: NonArchimedean Köthe spaces, isometrical isomorphy, Schauder basis. MSC: 46S10, 47S10, 46A35 [ Fulltextpdf (141 KB)] for subscribers only. 