International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 11, Pages 785-791
doi:10.1155/S0161171200002325

On some topological properties of generalized difference sequence spaces

Abstract

We obtain some topological results of the sequence spaces Δm(X), where Δm(X)={x=(xk):(Δmxk)∈X},   (m∈ℕ), and X is any sequence space. We compute the pα-, pβ-, and pγ-duals of l∞,c, and c0 and we investigate the N-(or null) dual of the sequence spaces Δm(l∞),   Δm(c), and Δm(c0). Also we show that any matrix map from Δm(l∞) into a BK-space which does not contain any subspace isomorphic to Δm(l∞) is compact.