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

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Abstract

In this paper, we introduce a new series space

|

N

p θ

|

(

μ)

as the set of all series summable by the absolute Norlund summability method, which includes the spaces

l( μ ),

|

C

λ

|

k and

|

N

p

θ

|

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,

α−, β−, γ −

¿

duals, Schauder basis, and characterize certain matrix transformations on that space.

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