A new double series space derived by factorable matrix and four-dimensional matrix transformations

In this study, we introduce a new double series space ${\left|F_{a,b}^{u,\theta }\right|}_k$ using the four dimensional factorable matrix $F$ and absolute summability method for $k\ge 1$. Also, examining some algebraic and topological properties of ${\left|F_{a,b}^{u,\theta }\right|}_k$, we show that it is norm isomorphic to the well-known double sequence space ${\mathcal{L}}_k$ for $1\le k<\mathrm{\infty }.$ Furthermore, we determine the $\alpha$-, $\beta \left(bp\right)$- and $\gamma$-duals of the spaces ${\left|F_{a,b}^{u,\theta }\right|}_k$ for $k\ge 1.$ Additionally, we characterize some new four dimensional matrix transformation classes on double series space ${\left|F_{a,b}^{u,\theta }\right|}_k$. Hence, we extend some important results concerned on Riesz and Cesàro matrix methods to double sequences owing to four dimensional factorable matrix.