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On some generalized difference sequence spaces. (English) Zbl 0841.46006
Summary: We define the sequence spaces $$\ell_\infty(\Delta^m)$$, $$c(\Delta^m)$$ and $$c_0(\Delta^m)$$ $$(m\in \mathbb{N})$$ where for instance $$\ell_\infty(\Delta^m)= \{x= (x_k): (\Delta^m x_k)\in \ell_\infty\}$$, 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.

##### MSC:
 46A45 Sequence spaces (including Köthe sequence spaces) 46A20 Duality theory for topological vector spaces 40C05 Matrix methods for summability 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)