Almost convergent sequence spaces derived by quadruple band matrix and geometric properties

In this work, almost convergent sequence spaces derived by means of a quadruple band matrix and geometric properties of the sequence space l_p (Q) are discussed. In this context, first of all, the studies on almost convergent sequence spaces in the literature were examined. Within the scope of the study, the concepts of quadruple band matrix and almost convergent sequence spaces, dual spaces, matrix transformations, matrix classes are discussed and the scope of the subject is expanded and enriched by including theorems and lemmas in previous studies. Later, in the study, the concepts of sequence spaces and matrix domain were discussed and almost convergent sequence spaces, almost null convergent sequence spaces and almost convergent series sequence spaces were constructed and their properties such as BK- spaces, isomorphic spaces, duals, Schauder bases and matrix classes were examined. Finally, in this study, information about some geometric properties of the sequence space l_p (Q) derived by the domain of quadruple band matrix is conveyed.