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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.30 no.3 Antofagasta dic. 2011 

Proyecciones Journal of Mathematics Vol. 30, No 3, pp. 369-399, December 2011. Universidad Católica del Norte Antofagasta - Chile


Schauder basis in a locally K — convex space and perfect sequence spaces

R. Ameziane Hassani, A. El Amrani

Universite Sidi Mohamen Ben Abdellah, Morocco


M. Babahmed

Universite Moulay Ismail, Morocco



In this work, we are dealing with the natural topology in a perfect sequence space and the transfert of topologies of a locally K — convex space E with a Schauder basis (ei)i to such Space. We are also interested with the compatible topologies on E for which the basis(ei)i is equicontinuous, and the weak basis problem. Finally, we give some applications to barrelled Spaces and G—Spaces.

Keywords : non archimedean analysis, locally K— convex spaces, Schauder basis, the weak basis theorem, compatible topologies, perfect sequence spaces, K— barrelled spaces and G- spaces.

AMS classification: 46S10


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R. Ameziane Hassani

Department of mathematics and computer science Faculty of Sciences Dhar Mahraz

B. P. 1796 Atlas Fàes,


e-mail :

A. El Amrani

Department of mathematics and computer science Faculty of Sciences Dhar Mahraz

B. P. 1796 Atlas Fàes,


e-mail :

M. Babahmed

Department of mathematics and computer science

Faculty of Sciences Meknes,


e-mail :

Received : July 2010. Accepted : September 2011