Generalization of the space l(p) derived by absolute Euler summability and matrix operators.

Abstract

The sequence space $l\left(p\right)$ 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 $l\left(p\right)$ to the space $\left|E_{\varphi }^r\right|\left(p\right)$ derived by the absolute summability of Euler mean. Also, we show that it is a paranormed space and linearly isomorphic to $l\left(p\right)$ . 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.