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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.
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