In the present paper, we introduce the absolute Fibonacci space $\left|F_u\right|_{k}$, give some inclusion relations and investigate topological and algebraic structure such as $BK$-space, $\alpha$-, $\beta$-, $\gamma$- duals and Schauder basis. Further, we characterize certain matrix and compact operators on these spaces, also determine their norms and Hausdroff meausures of noncompactness.