p. 273 - 280 The continuous dual of the sequence space lp(Dn ), (1 £ p £ ¥ , nÎ N ) M. Imaninezhad and M. Miri Received: February 12, 2010; Revised: June 16, 2010; Accepted: June 20, 2010 Abstract. The space lp(Dm ) consisting of all sequences whose m-th order differences are p-absolutely summable was recently studied by Altay. Following Altay, we have found the continuous dual of the spaces l1(Dn ) and lP(Dn ). We have also determined the norm of the operator Dn acting from l1 to itself and from l¥ to itself, and proved that Dn is a bounded linear operator on the space lp(Dn ). Keywords: difference operator; continuous dual; Banach space; sequence space; Schauder basis lp(Dn ) AMS Subject classification: Primary: 46B10 Secondary: 46B45 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2010, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |