Extension of Maddox's space l(mu) with Norlund means

Abstract

In this paper, we introduce a new series space |N_p^? |(µ)as the set of all series summable by the absolute Norlund summability method, which includes the spaces l(µ), |C_( ?) |_k and |N_p^? |_k of Maddox [Spaces of strongly summable sequences, Quart. J. Math. 18(1) (1967) 345-355], Sarigol [Spaces of series summable by absolute Cesaro and matrix operators, Comm. Math Appl. 7(1) (2016) 11-22], Hazar and Sarigol [On absolute Norlund 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, ?-,ß-,?-duals, Schauder basis, and characterize certain matrix transformations on that space.