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.
Highlights
The study of sequence spaces is generally initiated by problems in summability theory, Fourier series and power series
We study the sequence spaces which are generated by infinite matrices
The paranormed sequence spaces were introduced by Borwien, Bourgin, Simons, and later, Maddox developed it in considerable details
Summary
The study of sequence spaces is generally initiated by problems in summability theory, Fourier series and power series. We study certain topological properties like separability, completeness, and r -convexity of these generalized paranormed sequence spaces. All the corresponding results related to the sequence spaces c0, lp, c, l∞, and wp follow as special cases of the theorems established here.
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