F K-Spaces Containing Absolutely K-Summable Series Space and Matrix Operators

Abstract

In a later paper [34], the Banach space of all absolutely k-summable series has been introduced and studied by Sarıgöl and Agarwal. In the present paper, we introduce a paranormed space containing this space, following the Maddox papers [19–21], and show that it is an FK-space and isometrically isomorphic to the well-known space l(µ). We also establish the Schauder basis and α, β, γ duals of this space and qualify the related matrix operators. Our results include, as particular cases, a number of the well-known results in [3, 6–15, 24, 25, 28, 31, 33, 34]. © 2024 A. Razmadze Mathematical Institute of Iv. Javakhishvili Tbilisi State University. All rights reserved.