THE DUAL SPACE OF THE SEQUENCE SPACE bvp (1 ≤ p < ∞)

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 improve the presentation and are confirmed by last notations l1* = l∞ and lp* = lq.