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Domain of the double sequential band matrix in the classical sequence spaces

Research paper by Murat Candan

Indexed on: 05 Dec '12Published on: 05 Dec '12Published in: Journal of Inequalities and Applications



Abstract

Let λ denote any one of the classical spaces ℓ∞Open image in new window, c, c0Open image in new window and ℓpOpen image in new window of bounded, convergent, null and absolutely p-summable sequences, respectively, and λ˜Open image in new window also be the domain of the double sequential band matrix B(r˜,s˜)Open image in new window in the sequence space λ, where (rn)n=0∞Open image in new window and (sn)n=0∞Open image in new window are given convergent sequences of positive real numbers and 1≤p<∞Open image in new window. The present paper is devoted to studying the sequence space λ˜Open image in new window. Furthermore, the β- and γ-duals of the space λ˜Open image in new window are determined, the Schauder bases for the spaces c˜Open image in new window, c˜0Open image in new window and ℓ˜pOpen image in new window are given, and some topological properties of the spaces c˜0Open image in new window, ℓ˜1Open image in new window and ℓ˜pOpen image in new window are examined. Finally, the classes (λ˜1:λ2)Open image in new window and (λ˜1:λ˜2)Open image in new window of infinite matrices are characterized, where λ1∈{ℓ∞,c,c0,ℓp,ℓ1}Open image in new window and λ2∈{ℓ∞,c,c0,ℓ1}Open image in new window.MSC:46A45, 40C05.