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On some generalized difference sequence spaces. (English) Zbl 0841.46006
Summary: We define the sequence spaces (Δ m ), c(Δ m ) and c 0 (Δ m ) (m) where for instance (Δ m )={x=(x k ):(Δ m x k ) }, give some topological properties, inclusion relations of these spaces and compute their continuous and Köthe-Toeplitz duals. Furthermore, we characterize some matrix classes related to these sequence spaces. This study generalizes some results of the first author [Turk. J. Math. 17, No. 1, 18-24 (1993; Zbl 0826.40001)] and H. Kizmaz [Can. Math. Bull. 24, No. 2, 169-176 (1981; Zbl 0454.46010)] in special cases.

46A45Sequence spaces
46A20Duality theory of topological linear spaces
40C05Matrix methods in summability
47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)