A General study of Cesaro sequence spaces with Matrix transformations

Abstract

 In this paper, the researcher utilize the non-absolute type of Cesaro sequence space to transform the Cesaro sequence spaces and establish the necessary and sufficient conditions for the existence of an infinite matrix in the spaces ℓ_∞ and C, respectively. When the sequences x∈X satisfy the condition that the series Σ^∞_k=1 X_k converges, the sequence space H becomes a non-absolute Banach space that fulfills the fundamental requirements for transforming the Cesaro sequence space X_p into the corresponding spaces of ℓ_∞ and all convergent sequences. As a consequence of the matrix transformation, some theorems are derived.