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

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 | E ϕ r | ( 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.