International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 11, Pages 651-657
doi:10.1155/S0161171202109033

Local completeness of ℓp(E), 1≤p<∞

C. Bosch1 , T. Gilsdorf2 , C. Gómez1 and R. Vera4

1Departamento Académico de Matemáticas, Itam, Rio Hondo #1, Col. Tizapán San Ángel, C.P., México 01000 D.F., Mexico
 2Department of Mathematics, University of North Dakota, Grand Forks 58202-8376, ND, USA
 4Esc. de C. Físico-Matemáticas, Universidad Michoacana, Santiago Tapia No. 403 Edif. B, Ciudad Universitaria, Morelia 58060, Mich., Mexico

Abstract

We study the heredity of local completeness and the strict Mackey convergence property from the locally convex space E to the space of absolutely p-summable sequences on E, ℓp(E) for 1≤p<∞.