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. Bosch,1 T. Gilsdorf,2 C. Gómez,1 and R. Vera3

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
3Esc. de C. Físico-Matemáticas, Universidad Michoacana, Santiago Tapia No. 403 Edif. B, Ciudad Universitaria, Morelia 58060, Mich., Mexico

Received 10 September 2001; Revised 26 February 2002

Copyright © 2002 C. Bosch et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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<∞.