International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 9, Pages 547-560
doi:10.1155/S0161171201005166

Vector-valued sequence spaces generated by infinite matrices

Nandita Rath

Department of Mathematics and Statistics, University of Western Australia, Nedlands, Australia

Abstract

Let A=(ank) be an infinite matrix with all ank≥0 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.