Polar topologies on sequence spaces in non-archimedean analysis

R. Ameziane Hassani*, A. El Amrani*, M. Babahmed**

* Universite Sidi Mohamed Ben Abdellah, Morocco

** Universite Moulay Ismail, Morocco

ABSTRACT

The purpose of the present paper is to develop a theory of a duality in sequence spaces over a non-archimedean vector space. We introduce polar topologies in such spaces, and we give basic results characterizing compact, C-compact, complete and AK —complete subsets related to these topologies.

Keywords : Locally K-convex topologies, non archimedean sequence spaces, Schauder basis, separated duality.

REFERENCES

[1] R. Ameziane Hassani, M. Babahmed, Topologies polaires compatibles avec une dualiteseparante sur un corps valuenon-Archimedien, Proyecciones Vol. 20, Num. 2, pp. 217-240, (2001).

[2] H.R. Chillingworth, Generalised "dual" sequence spaces, Ned. Akad. Proc. Ser. A. 61, pp. 307-515, (1958).

[3] A. El amrani, R. Ameziane Hassani and M. Babahmed, Topologies on sequence spaces in non-archimedean analysis, J. of Mathematical Sciences: Advances and Applications Vol. 6, Num. 2, pp.193-214, (2010).

[4] T. Komura; Y. Komura, sur les espaces parfaits de suites et leurs generalisations, J. Math. Soc. Japon. 15, pp. 319-338, (1963).

[5] G. Kothe, Topological vector spaces, Springer-Verlag Berlin Heidlberg New york, (1969).

[6] -----------, Neubegrundung der theorie der vollkommen Raume, Math. Nach. 4, pp. 70-80, (1951).

[7] -----------;O.Toeplitz, LineareRaume mit unendlich vielen Koordi-naten und Ringe unendlicher Matrizen, J. reine angew. Math. 171, pp. 193-226, (1934).

[8] G. Matthews, Generalised Rings of infinite matrices, Ned. Akad. Wet. Proc. 61, pp. 298-306 (1958).

[9] A.F.Monna, Analyse non-archimedienne, Springer-Verlag Berlin New York Heidelberg (1970).         [  ]

[10] H.H. Schaefer, Topological vector spaces, Springer-Verlag Berlin New york Heidlberg, (1971).

[11] W. H. Schikhof, Locally convex spaces over nonspherically complete valued field Bull. Soc.Math. Belg.Ser. B. 38, pp. 187-224, (1986).

[12] J. Van Tiel, Espaces localement K-convexes I-III, Indag. Math. 27,pp. 249-289 (1965).

Received : May 2011. Accepted : January 2012

R. Ameziane Hassani

Departement de Mathematiques

Faculte des Sciences

Dhar El Mehraz

B. P. 1796 FES - MAROC

e-mail : ramezianehassani@hotmail.com

A. El Amrani

Departement de Mathematiques

Faculte des Sciences Dhar El Mehraz

Universite Sidi Mohamed Ben Abdellah

B. P. 1796, FES - MAROC

e-mail : ramezianehassani@hotmail.com

M. Babahmed

Departement de Mathematiques

Faculte des Sciences de Meknes

Universite Moulay Ismail

B. P. 11201 Zitoune

MEKNES - MAROC

e-mail : babahmed@fs-umi.ac.ma