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The Dual Spaces of the Sets of Difference Sequences of Order $m$  
 
  Authors: C.A. Bektas, Mikhail Et,  
  Keywords: Difference sequences, $alpha -$, $beta -$ and $gamma -$duals.  
  Date Received: 16/12/05  
  Date Accepted: 07/01/06  
  Subject Codes:

40C05, 46A45.

  
  Editors: Alexander G. Babenko,  
 
  Abstract:

The idea of difference sequence spaces was introduced by Kizmaz [5] and the concept was generalized by Et and Çolak [3]. Let $ p=(p_{k})$ be a bounded sequence of positive real numbers and $ v=(v_{k})$ be any fixed sequence of non-zero complex numbers. If $ x=(x_{k})$ is any sequence of complex numbers we write $ Delta _{v}^{m}x$ for the sequence of the $ m$ -th order differences of $ x$ and $ Delta _{v}^{m}(X)={x=(x_{k}):Delta _{v}^{m}xin X}$ for any set $ X$ of sequences. In this paper we determine the $ alpha $ -, $ beta $ - and $ gamma $ - duals of the sets $ Delta _{v}^{m}(X)$ which are defined by Et et al. [2] for $ X=ell _{infty }(p)$, $ c(p) $ and $ c_{0}(p).$ This study generalizes results of Malkowsky [9] in special cases. ;


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