Proyecciones Journal of Mathematics Vol. 30, N^o 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

 

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ABSTRACT

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 (e_i)_i to such Space. We are also interested with the compatible topologies on E for which the basis(e_i)_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,

Morocco

e-mail : ra.ameziane@yahoo.fr

A. El Amrani

Department of mathematics and computer science Faculty of Sciences Dhar Mahraz

B. P. 1796 Atlas Fàes,

Morocco

e-mail : abdelkhalek-amrani@hotmail.com

M. Babahmed

Department of mathematics and computer science

Faculty of Sciences Meknes,

Morocco

e-mail : babahmed@hotmail.com

Received : July 2010. Accepted : September 2011