ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE




Vol. LXXIX, 1 (2010)
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.



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Acta Mathematica Universitatis Comenianae
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