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Zbl 1123.46007
Malkowsky, Eberhard; Mursaleen, M.; Suantai, Suthep
The dual spaces of sets of difference sequences of order $m$ and matrix transformations. (English)
[J] Acta Math. Sin., Engl. Ser. 23, No. 3, 521-532 (2007). ISSN 1439-8516; ISSN 1439-7617/e

Summary: Let $p = (p_k)^{\infty }_{k = 0}$ be a bounded sequence of positive reals, $m\in \Bbb N$, and $u$ be s sequence of nonzero terms. If $x =(x_{k})^{\infty }_{k = 0}$ is any sequence of complex numbers, we write $\Delta ^{(m)} x$ for the sequence of the $m$-th order differences of $x$ and $\Delta ^{( m)}_{u} X = \{x = (x)^{\infty }_{k = 0} :u\Delta ^{(m)} x \in X\}$ for any set $X$ of sequences. We determine the $\alpha$-, $\beta$- and $\gamma$-duals of the sets $\Delta ^{(m)}_{u} X$ for $X = c_{0}(p), c(p), \ell _\infty (p)$ and characterize some matrix transformations between these spaces $\Delta ^{(m)} X$.

MSC 2000:: *46A45 Sequence spaces
40H05 Functional analytic methods in summability

Keywords: difference sequences; dual spaces; matrix transformations

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