Basar, FeyziRoopaei, Hadi2024-08-042024-08-0420230252-96021572-9087https://doi.org/10.1007/s10473-023-0404-0https://hdl.handle.net/11616/101412Let the triangle matrix A(ru) be a generalization of the Cesaro matrix and U & ISIN; {c(0), c, l(& INFIN;)}. In this study, we essentially deal with the space U(A(ru)) defined by the domain of A(ru) in the space U and give the bases, and determine the Kothe-Toeplitz, generalized Kothe-Toeplitz and bounded-duals of the space U (A(ru)). We characterize the classes (l(& INFIN;) (A(ru)):l(& INFIN;)), (l(& INFIN;)(A(ru)): c), (c(A(ru)): c), and (U: V(A(ru))) of infinite matrices, where V denotes any given sequence space. Additionally, we also present a Steinhaus type theorem. As an another result of this study, we investigate the l(p)-norm of the matrix A(ru) and as a result obtaining a generalized version of Hardy's inequality, and some inclusion relations. Moreover, we compute the norm of well-known operators on the matrix domain l(p) (A(ru)).eninfo:eu-repo/semantics/closedAccessmatrix domainnormed sequence spaceduals and matrix transformationsArticle4341518153610.1007/s10473-023-0404-02-s2.0-85162021553Q2WOS:001012601800004Q1