Generalization of the Absolute Cesàro Space and Some Matrix Transformations. (4th July 2019) - Gökçe, Fadime; Sarıgöl, Mehmet Ali
Abstract: The space ℓ k was extended to the space ℓ ( p ) by Maddox, where p = ( p n ) is a bounded sequence of positive numbers. The series space | C λ, μ | k has more recently been studied by Hazar and Sarıgöl. In this article, following Maddox we derived a more general series space | C λ, μ | ( p ) and show that it is a paranormed space and linearly isomorphic to the space ℓ ( p ) . Also, we construct its α −, β −, γ − duals and Schauder basis. Further, we characterize the classes of certain matrix transformations on that space and obtain some well-known results as a particular case.