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.