International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 341-356
doi:10.1155/S0161171295000433

Topological properties and matrix transformations of certain ordered generalized sequence spaces

Abstract

In this note, we carry out investigations related to the mixed impact of ordering and topological structure of a locally convex solid Riesz space (X,τ) and a scalar valued sequence space λ, on the vector valued sequence space λ(X) which is formed and topologized with the help of λ and X, and vice versa. Besides,we also characterize o-matrix transformations from c(X), ℓ∞(X) to themselves, cs(X) to c(X) and derive necessary conditions for a matrix of linear operators to transform ℓ1(X) into a simple ordered vector valued sequence space Λ(X).