Abstract
The sequence spaces $\ell_\infty(p)$, $c(p)$ and $c_0(p)$ were introduced and studied by Maddox [Proc. Cambridge Philos. Soc. 64 (1968), 335-340]. In the present paper, we introduce the sequence spaces $\ell_\infty(B,p)$, $c(B,p)$ and $c_0(B,p)$ of non-absolute type which are derived by the triple band matrix $B(r,s,t)$ and is proved that the spaces $\ell_\infty(B,p)$, $c(B,p)$ and $c_0(B,p)$ are paranorm isomorphic to the spaces $\ell_\infty(p)$, $c(p)$ and $c_0(p)$; respectively. Besides this, the $\alpha$-, $\beta$- and $\gamma$-duals of the spaces $\ell_\infty(B,p)$, $c(B,p)$ and $c_0(B,p)$ are computed and the bases of the spaces $c(B,p)$ and $c_0(B,p)$ are constructed. Finally, the matrix mappings from the sequence spaces $\lambda(B,p)$ to a given sequence space $\mu$ and from the sequence space $\mu$ to the sequence space $\lambda(B,p)$ are characterized, where $\lambda\in\{\ell_\infty,c,c_0\}$.
Citation
Feyzi Başar. Ahmet Faruk Çakmak. "Domain of the triple band matrix on some Maddox's spaces." Ann. Funct. Anal. 3 (1) 32 - 48, 2012. https://doi.org/10.15352/afa/1399900022
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