ON SOME DISTINGUISHED SUBSPACES AND RELATIONSHIP BETWEEN DUALS

Abstract

In this paper, we observe some new spaces to obtain new β- and γtype duality of a sequence space λ, related to the some sequence spaces. Beforethis we give some new distinguished subspaces of an F K space obtained by anoperator of Ayd n and Ba³ar [2], which is stronger than common C- Cesàro operator. We also give some structural theorems and inclusions for these distinguishedsubspaces. Finally we prove some theorems related to the f-, ar- and ar- duality ofa sequence space λ like Goes [14] and Buntinas [8]. These theorems are importantsb to decade the duality of a sequence space in summability theory and topologicalsequence spaces theory