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Proyecciones (Antofagasta)

versão impressa ISSN 0716-0917

Proyecciones (Antofagasta) vol.31 no.2 Antofagasta jun. 2012

http://dx.doi.org/10.4067/S0716-09172012000200002 

Proyecciones Journal of Mathematics Vol. 31, No 2, pp. 103-123, June 2012. Universidad Católica del Norte Antofagasta - Chile

 

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.

MSC2010 : 11F85 - 46A03 - 46A20 - 46A22 - 46A35 - 46A45 -464A50.


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).

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[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).         [ Links ]

[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

Universite Sidi Mohamed Ben Abdellah

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