Hostname: page-component-76d6cb85b7-lcgwf Total loading time: 0 Render date: 2026-07-14T06:58:27.907Z Has data issue: false hasContentIssue false
  • English
  • Français

On Quotients of Non-Archimedean Köthe Spaces

Published online by Cambridge University Press:  20 November 2018

Wiesław Śliwa
Wiesław Śliwa*
Affiliation:
Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland e-mail: sliwa@amu.edu.pl
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We show that there exists a non-archimedean Fréchet-Montel space $W$ with a basis and with a continuous norm such that any non-archimedean Fréchet space of countable type is isomorphic to a quotient of $W$ . We also prove that any non-archimedean nuclear Fréchet space is isomorphic to a quotient of some non-archimedean nuclear Fréchet space with a basis and with a continuous norm.

Keywords

46S1046A45Non-archimedean Köthe spacesnuclear Fréchet spacespseudo-bases

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 1 , 01 March 2007 , pp. 149 - 157
Copyright
Copyright © Canadian Mathematical Society 2007

References

[1] De Grande-De Kimpe, N., Non-archimedean Fréchet spaces generalizing spaces of analytic functions. Nederl. Akad.Wetensch. Indag. Mathem. 44(1982), 423–439.Google Scholar
[2] De Grande-De Kimpe, N., Kąkol, J., Perez-Garcia, C. and Schikhof, W. H., Orthogonal sequences in non-archimedean locally convex spaces. Indag. Mathem. N.S. 11(2000), 187–195.Google Scholar
[3] De Grande-De Kimpe, N., Ka¸kol, J., Perez-Garcia, C. and Schikhof, W. H., Orthogonal and Schauder bases in non-archimedean locally convex spaces. In: p-adic Functional canalysis, Lecture Notes in Pure and Appl. Math. 222, Dekker, New York, 2001, 103–126.Google Scholar
[4] Prolla, J. B., Topics in Functional Analysis over Valued Division Rings. North-Holland Math. Studies 77, North-Holland, Amsterdam, 1982.Google Scholar
[5] van Rooij, A. C. M., Non-Archimedean functional analysis. Monographs and Textbooks in Pure and Applied Math. 51, Marcel Dekker, New York, 1978.Google Scholar
[6] Schikhof, W. H., Locally convex spaces over non-spherically complete valued fields. I-II. Bull. Soc. Math. Belg. 38(1986), 187–207, 208–224.Google Scholar
[7] Schikhof, W. H., Minimal-Hausdorff p-adic locally convex spaces. Ann. Math. Blaise Pascal, 2(1995), 259–266.Google Scholar
[8] Śliwa, W., Examples of non-Archimedean nuclear Fréchet spaces without a Schauder basis. Indag. Math. 11(2000), 607–616.Google Scholar
[9] Śliwa, W., Closed subspaces without Schauder bases in non-archimedean Fréchet spaces. Indag. Math. 12(2001), 261–271.Google Scholar
[10] Śliwa, W., On closed subspaces with Schauder bases in non-Archimedean Fréchet spaces. Indag.Math. 12(2001), 519–531.Google Scholar
[11] Śliwa, W., On the quasi-equivalence of orthogonal bases in non-Archimedean metrizable locally convex spaces. Bull. Belg. Math. Soc. Simon Stevin 9(2002), 465–472.Google Scholar
[12] Śliwa, W., On universal Schauder bases in non-archimedean Fréchet spaces. Canad. Math. Bull. 47(2004), 108–118.Google Scholar