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Zbl 0679.46005
Sarigöl, M.Ali
On difference sequence spaces.
(English)
[J] J. Karadeniz Tech. Univ., Fac. Arts Sci., Ser. Math.-Phys. 10, 63-71 (1987).

Summary: We defne the spaces $\ell\sb{\infty}(\Delta\sb q)$, $c(\Delta\sb q)$ and $c\sb 0(\Delta\sb q)$, $q<1$, where for example $\ell\sb{\infty}(\Delta\sb q)=\{x=(x\sb k):$ $k\sp q(x\sb k-x\sb{k+1})\in \ell\sb{\infty}\}$, and compute there duals ($\alpha$-dual, $\beta$-dual and $\gamma$-dual). We also determine necessary and sufficient conditions for a matrix A to map $\ell\sb{\infty}(\Delta\sb q)$ or $c(\Delta\sb q)$ into $\ell\sb{\infty}$ or c. Our results includes some results of {\it H. Kizmaz} [Can. Math. Bull. 24, 169-176 (1981; Zbl 0454.46010)] as a special case.
MSC 2000:
*46A45 Sequence spaces
47B37 Operators on sequence spaces, etc.

Keywords: $\alpha$-dual; $\beta$-dual; $\gamma$-dual

Citations: Zbl 0454.46010

Cited in: Zbl 1091.40001

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