<i>fk</I>-spaces Containing Absolutely<i> K</I>-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 Sar & imath;go<spacing diaeresis>l 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 ( mu ). We also establish the Schauder basis and alpha, beta, gamma 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].