Geodesic
On Quotients of Non-Archimedean Köthe Spaces
Canadian mathematical bulletin, Tome 50 (2007) no. 1, pp. 149-157

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2007-015-0
Mots-clés : 46S10, 46A45, Non-archimedean Köthe spaces, nuclear Fréchet spaces, pseudo-bases 
Śliwa, Wiesław. On Quotients of Non-Archimedean Köthe Spaces. Canadian mathematical bulletin, Tome 50 (2007) no. 1, pp. 149-157. doi: 10.4153/CMB-2007-015-0
@article{10_4153_CMB_2007_015_0,
     author = {\'Sliwa, Wies{\l}aw},
     title = {On {Quotients} of {Non-Archimedean} {K\"othe} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {149--157},
     year = {2007},
     volume = {50},
     number = {1},
     doi = {10.4153/CMB-2007-015-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-015-0/}
}
TY  - JOUR
AU  - Śliwa, Wiesław
TI  - On Quotients of Non-Archimedean Köthe Spaces
JO  - Canadian mathematical bulletin
PY  - 2007
SP  - 149
EP  - 157
VL  - 50
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-015-0/
DO  - 10.4153/CMB-2007-015-0
ID  - 10_4153_CMB_2007_015_0
ER  - 
%0 Journal Article
%A Śliwa, Wiesław
%T On Quotients of Non-Archimedean Köthe Spaces
%J Canadian mathematical bulletin
%D 2007
%P 149-157
%V 50
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-015-0/
%R 10.4153/CMB-2007-015-0
%F 10_4153_CMB_2007_015_0

[1] [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] [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] [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] [4] Prolla, J. B., Topics in Functional Analysis over Valued Division Rings. North-Holland Math. Studies 77, North-Holland, Amsterdam, 1982. Google Scholar

[5] [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] [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] [7] Schikhof, W. H., Minimal-Hausdorff p-adic locally convex spaces. Ann. Math. Blaise Pascal, 2(1995), 259–266. Google Scholar

[8] [8] Śliwa, W., Examples of non-Archimedean nuclear Fréchet spaces without a Schauder basis. Indag. Math. 11(2000), 607–616. Google Scholar

[9] [9] Śliwa, W., Closed subspaces without Schauder bases in non-archimedean Fréchet spaces. Indag. Math. 12(2001), 261–271. Google Scholar

[10] [10] Śliwa, W., On closed subspaces with Schauder bases in non-Archimedean Fréchet spaces. Indag.Math. 12(2001), 519–531. Google Scholar

[11] [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] [12] Śliwa, W., On universal Schauder bases in non-archimedean Fréchet spaces. Canad. Math. Bull. 47(2004), 108–118. Google Scholar

Cité par Sources :