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 Manjul Gupta and Kalika Kaushal. 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 and a scalar valued sequence space , on the vector
valued sequence space which is formed and topologized with the help
of and , and vice versa. Besides,we also characterize -matrix transformations
from , to themselves, to and derive necessary
conditions for a matrix of linear operators to transform into a
simple ordered vector valued sequence space .