New Matrix Domain Derived by the Matrix Product

Vatan Karakaya, Necip Şimşek, Kadri Doğan

In this work, we define new sequence spaces by using the matrix obtained by product of factorable matrix and generalized difference matrix of order $m$. Afterward, we investigate topological structure which are completeness, $A$K-property, $AD$-property. Also, we compute the $\alpha$-, $\beta$- and $\gamma$-duals, and obtain bases for these sequence spaces. Finally we give necessary and sufficient conditions on matrix transformation between these new sequence spaces and $c,\ell_\infty$.