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International Journal of Mathematics and Mathematical Sciences
Volume 26, 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 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.


Let A=(ank) be an infinite matrix with all ank0 and P a bounded, positive real sequence. For normed spaces E and Ek the matrix A generates paranormed sequence spaces such as [A,P]((Ek)), [A,P]0((Ek)), and [A,P](E) which generalize almost all the existing sequence spaces, such as l, c0, c, lp, wp, and several others. In this paper, conditions under which these three paranormed spaces are separable, complete, and r-convex, are established.