p. 143 - 149 The dual space of the sequence space bvp (1 £ p < ¥) M. Imaninezhad and M. Miri Received: August 26, 2009; Accepted: September 29, 2009 Abstract. The sequence space bvp consists of all sequences (xk) such that (xk - xk - 1) belongs to the space lp. The continuous dual of the sequence space bvp has recently been introduced by Akhmedov and Basar [Acta Math. Sin. Eng. Ser., 23(10), 2007, 1757 - 1768]. In this paper we show a counterexample for case p = 1 and introduce a new sequence space d¥ instead of d1 and show that bv1* = d¥. Also we have modified the proof for case p > 1. Our notations improves the presentation and confirms with last notations l1* = l¥ and l1* = lq. Keywords: dual space; sequence space; Banach space; isometrically isomorphic. 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 © 2009, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |