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

On some topological properties of generalized difference sequence spaces

Department of Mathematics, Firat University, Elazig 23119, Turkey

Received 22 October 1998; Revised 12 June 2000

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We obtain some topological results of the sequence spaces Δm(X), where Δm(X)={x=(xk):(Δmxk)X},(m), 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.