Extension of Maddox’s space l(μ) with Nörlund means

Abstract

In this paper, we introduce a new series space [Formula: see text] as the set of all series summable by the absolute Nörlund summability method, which includes the spaces [Formula: see text] and [Formula: see text] of Maddox [Spaces of strongly summable sequences, Quart. J. Math. 18(1) (1967) 345–355], Sarıgöl [Spaces of series summable by absolute Cesàro and matrix operators, Comm. Math Appl. 7(1) (2016) 11–22], Hazar and Sarıgöl [On absolute Nörlund spaces and matrix operators, Acta Math. Sinica, (English Ser.) 34(5) (2018) 812–826], respectively. Also, we study its some algebraic and topological structures such as isomorphism, the [Formula: see text], [Formula: see text], [Formula: see text] duals, Schauder basis, and characterize certain matrix transformations on that space.