Abstract
The sequence space l(p) having an important role in summability theory was defined and studied by Maddox (Q. J. Math. 18:345–355, 1967). In the present paper, we generalize the space l(p) to the space vert E_{phi }^{r} vert (p) derived by the absolute summability of Euler mean. Also, we show that it is a paranormed space and linearly isomorphic to l(p). Further, we determine α-, β-, and γ-duals of this space and construct its Schauder basis. Also, we characterize certain matrix operators on the space.
Highlights
1 Introduction Let X, Y be any subsets of ω, the set of all sequences of complex numbers, and A = be an infinite matrix of complex numbers
If Ax ∈ Y, whenever x ∈ X, A, denoted by A : X → Y, is called a matrix transformation from X into Y, and we mean the class of all infinite matrices A such that A : X → Y by (X, Y )
The matrix domain of an infinite matrix A in a sequence space X is defined by XA = x = ∈ ω : A(x) ∈ X
Summary
The matrix domain of an infinite matrix A in a sequence space X is defined by XA = x = (xn) ∈ ω : A(x) ∈ X . Lemma 2.2 ([33]) Let A = (anv) be an infinite matrix with complex numbers and (pv) be a bounded sequence of positive numbers.
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