Domain of the Double Sequential Band Matrix B(r~,s~) in the Sequence Space ℓ(p)

The sequence space ℓ(p) was introduced by Maddox (1967). Quite recently, the domain of the generalized difference matrix B(r,s) in the sequence space ℓp has been investigated by Kirişçi and Başar (2010). In the present paper, the sequence space ℓ(B~,p) of nonabsolute type has been studied which is the domain of the generalized difference matrix B(r~,s~) in the sequence space ℓ(p). Furthermore, the alpha-, beta-, and gamma-duals of the space ℓ(B~,p) have been determined, and the Schauder basis has been given. The classes of matrix transformations from the space ℓ(B~,p) to the spaces ℓ∞, c and c0 have been characterized. Additionally, the characterizations of some other matrix transformations from the space ℓ(B~,p) to the Euler, Riesz, difference, and so forth sequence spaces have been obtained by means of a given lemma. The last section of the paper has been devoted to conclusion.