On Almost Convergence and Difference Sequence Spaces of Order m with Core Theorems

This paper is mainly concerned with introducing the spaces f s(Δ sup (m) /sup ), f (Δ sup (m) /sup ) and f sub 0 /sub (Δ sup (m) /sup ) that consist of all sequence whose (Δ sup (m) /sup ) transforms are in the set of almost convergent sequence and series spaces. Certain topological properties of these new almost convergent sets have been investigated as well as γ-- and β--duals of the spaces f s(Δ sup (m) /sup ) and f (Δ sup (m) /sup ). In addition to that the non-existence of Schauder basis of the spaces f s and f s(Δ sup (m) /sup ) is shown. Furthermore, the characterization of certain matrix classes on/into the sets of generalized difference almost convergent sequence and series has exhaustively been examined. Finally, some identities and inclusion relations related to core theorems are established.