Some new sequence spaces generated by Cesaro matrix of order 𝑚 and related results

Let 0 < 𝑝 < ∞. We essentially examine the sequence spaces 𝐶𝑚𝑝 and 𝐶∞𝑚 generated by the domain of the Cesàro matrix 𝐶𝑚 of order 𝑚 in the spaces ℓ𝑝 and ℓ∞ of absolutely 𝑝-summable and bounded sequences, respectively. We give some inclusion relation concerning to the spaces 𝐶𝑚𝑝 and 𝐶∞𝑚, and determine the 𝛼-, 𝛽- and 𝛾-duals of the spaces 𝐶1𝑚, 𝐶𝑚𝑝 and 𝐶∞𝑚. After more, we characterize the classes of matrix transformations from the spaces 𝐶𝑚𝑝 and 𝐶∞𝑚 to any one of the classical spaces 𝑐0, 𝑐 and ℓ∞, where 0 < 𝑝 < ∞. We also give some knowledge about Steinhaus-type theorems and present this type theorem. Finally, we establish some identities or estimates for the operator norms and the Hausdorff measures of non-compactness of certain matrix operators on the spaces 𝐶𝑚𝑝 and 𝐶∞𝑚 for 1 ≤ 𝑝 < ∞.Mathematics SubjectClassification(2020):46A45 40C05