Resumen

AMEZIANE HASSANI, R; EL AMRANI, A  y  BABAHMED, M. Schauder basis in a locally K - convex space and perfect sequence spaces. Proyecciones (Antofagasta) [online]. 2011, vol.30, n.3, pp. 369-399. ISSN 0716-0917.  doi: 10.4067/S0716-09172011000300007.

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.

Palabras clave : non archimedean analysis; locally K- convex spaces; Schauder basis; the weak basis theorem; compatible topologies; perfect sequence spaces; K- barrelled spaces and G- spaces.