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).

Keywords

• Riesz spaces
• order complete
• ideal
• diagonal property; positive
• sequentially order continuous and o-precompact linear operators; locally convex solid Riesz spaces
• Riesz seminorms
• Lebesgue
• pre-Lebesgue
• Fatau property; ordered vector valued sequence spaces
• matrix transformations.