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may 2020 On block basic sequences in non-Archimedean Köthe spaces
Wiesław Śliwa, Agnieszka Ziemkowska-Siwek
Bull. Belg. Math. Soc. Simon Stevin 27(1): 7-16 (may 2020). DOI: 10.36045/bbms/1590199299

Abstract

We prove that any two Schauder bases $(x_n)$ and $(y_n)$ in non-normable Köthe spaces $E$ and $F$ (over a non-Archimedean field $\mathbb K$) have block basic sequences $(u_n)$ and $(v_n)$, respectively, that are equivalent. Moreover we show that any Schauder basis in a non-normable Köthe space has a block basic sequence that is equivalent to the coordinate Schauder basis in some generalized power series space of infinite type; the generalized power series spaces are the most known and important examples of nuclear Köthe spaces. It follows that any two non-normable Köthe spaces $E$ and $F$, have closed subspaces $E_0$ and $F_0$, respectively, that are isomorphic to the same generalized power series space of infinite type $D_g(a,\infty)$ for some $g\in \Phi_c$ and $a\in \Gamma$.

Citation

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Wiesław Śliwa. Agnieszka Ziemkowska-Siwek. "On block basic sequences in non-Archimedean Köthe spaces." Bull. Belg. Math. Soc. Simon Stevin 27 (1) 7 - 16, may 2020. https://doi.org/10.36045/bbms/1590199299

Information

Published: may 2020
First available in Project Euclid: 23 May 2020

zbMATH: 07213653
MathSciNet: MR4102696
Digital Object Identifier: 10.36045/bbms/1590199299

Subjects:
Primary: 46A04, 46A35, 46A45, ‎46S10

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 1 • may 2020
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