Some new sequence spaces generated by Cesaro matrix of order ๐ and related results
Year: 2026
Type: article
Abstract: Let 0 < ๐ < โ. We essentially examine the sequence spaces ๐ถ๐๐ and ๐ถโ๐ generated by the domain of the Cesร ro matrix ๐ถ๐ of order ๐ in the spaces โ๐ and โโ of absolutely ๐-summable and bounded sequences, respectively. We give some inclusion relation concerning to the spaces ๐ถ๐๐ and ๐ถโ๐, and determine the ๐ผ-, ๐ฝ- and ๐พ-duals of the spaces ๐ถ1๐, ๐ถ๐๐ and ๐ถโ๐. After more, we characterize the classes of matrix transformations from the spaces ๐ถ๐๐ and ๐ถโ๐ to any one of the classical spaces ๐0, ๐ and โโ, where 0 < ๐ < โ. 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 ๐ถ๐๐ and ๐ถโ๐ for 1 โค ๐ < โ.Mathematics SubjectClassification(2020):46A45 40C05
Source: Istanbul Journal of Mathematics
Institutions: Inonu University, Usak University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7166706927