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On some topological properties of generalized difference sequence spaces

DOI: 10.1155/s0161171200002325

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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.

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