International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 9, Pages 547-560
Vector-valued sequence spaces generated by infinite matrices
Department of Mathematics and Statistics, University of Western Australia, Nedlands, Australia
Received 24 April 2000
Copyright © 2001 Nandita Rath. 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.
Let be an infinite matrix with all and a bounded, positive real sequence. For normed spaces and the matrix generates paranormed sequence spaces such as , , and which generalize almost all the existing sequence spaces, such as , , , , , and several others. In this paper, conditions under which these three paranormed spaces are separable, complete, and -convex, are established.