Candan, Murat2024-08-042024-08-0420222645-8845https://doi.org/10.33401/fujma.1003752https://search.trdizin.gov.tr/yayin/detay/507923https://hdl.handle.net/11616/88972This study serves for analysing algebraic and topological characteristics of the sequence spaces $X(widehat{widehat{B}}(r,s))$ constituted by using non-zero real number $r$ and $s$, where $X$ denotes arbitrary of the classical sequence spaces $ell_{infty}, c, c_{0} $ and $ell_{p}$ $(1<p<infty)$ of bounded, convergent, null and absolutely $p$-summable sequences, respectively and $X(widehat{widehat{B}})$ also is the domain of the matrix $widehat{widehat{B}}(r,s)$ in the sequence space $X$. Briefly, the $beta$- and $gamma$-duals of the space $X(widehat{widehat{B}})$ are computed, and Schauder bases for the spaces $c(widehat{widehat{B}})$, $c_{0}(widehat{widehat{B}})$ and $ell_{p}(widehat{widehat{B}})$ are determined, and some algebraic and topological properties of the spaces $c_{0}(widehat{widehat{B}})$, $ell_{1}(widehat{widehat{B}})$ and $ell_{p}(widehat{widehat{B}})$ are studied. Additionally, it is observed that all these spaces have some remarkable features, including the classes $(X_{1}(widehat{widehat{B}})$: $X_{2})$ and $(X_{1}(widehat{widehat{B}}): X_{2}(widehat{widehat{B}}))$ of infinite matrices which are characterized, in which $X_{1}in{ ell_{infty},c,c_{0},ell_{p},ell_{1}}$ and $X_{2}in{ell_{infty},c,c_{0},ell_{1}}$.eninfo:eu-repo/semantics/openAccessArticle51516210.33401/fujma.1003752507923