  The space $\widehat{\ell }_k$ of absolutely almost convergent series was
introduced and studied by Das et al [4]; which plays an important role in
summability theory, approximation theory, Fourier analysis, etc. In the present
paper we generalize the space making use of some factors and weighted mean
transformations, investigate its topological structures and relations between
classical sequence spaces. Also we characterize certain matrix operators on it.
