DOI: 10.26650/ijmath.2026.00032 ISSN: 2980-3020

Some new sequence spaces generated by Cesaro matrix of order π‘š and related results

Feyzi Başar, Medine Yeşilkayagil Savaşçı
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Let 0 < 𝑝 < ∞. We essentially examine the sequence spaces πΆπ‘šπ‘ and πΆβˆžπ‘š generated by the domain of the CesΓ ro matrix πΆπ‘š of order π‘š in the spaces ℓ𝑝 and β„“βˆž of absolutely 𝑝-summable and bounded sequences, respectively. We give some inclusion relation concerning to the spaces πΆπ‘šπ‘ and πΆβˆžπ‘š, and determine the 𝛼-, 𝛽- and 𝛾-duals of the spaces 𝐢1π‘š, πΆπ‘šπ‘ and πΆβˆžπ‘š. After more, we characterize the classes of matrix transformations from the spaces πΆπ‘šπ‘ and πΆβˆžπ‘š to any one of the classical spaces 𝑐0, 𝑐 and β„“βˆž, 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 πΆπ‘šπ‘ and πΆβˆžπ‘š for 1 ≀ 𝑝 < ∞.Mathematics SubjectClassification(2020):46A45 40C05

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