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International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 341-356

Topological properties and matrix transformations of certain ordered generalized sequence spaces

Department of Mathematics, Indian Institute of Technology, Kanpur 208016, India

Received 17 December 1991

Copyright © 1995 Hindawi Publishing Corporation. 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.


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), (X) to themselves, cs(X) to c(X) and derive necessary conditions for a matrix of linear operators to transform 1(X) into a simple ordered vector valued sequence space Λ(X).