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Zbl 1173.47021
Altay, Bilâl; Başar, Feyzi
The fine spectrum and the matrix domain of the difference operator $\Delta$ on the sequence space $l_{p},\ (0<p<1)$. (English)
[J] Commun. Math. Anal. 2, No. 2, 1-11, electronic only (2007). ISSN 1938-9787/e

The authors study the fine spectrum and the matrix domain $bv_{p}$, $0<p<1$, of the difference operator $\Delta$ in the sequence space $\ell_{p}$. They prove that $bv_{p}$ is a $p$-normed space and is linearly isomorphic to the space $\ell _{p}$. Finally, the $\beta$- and $\gamma$-duals of the space $bv_{p}$ are computed and the characterization of the matrix mappings from the space $bv_{p}$ into $\mu$ and from $\mu$ into $bv_{p}$ is given, where $\mu$ is any given sequence space.
[Bilender P. Allahverdiev (Isparta)]

MSC 2000:: *47B39 Difference operators (operator theory)
47A10 Spectrum and resolvent of linear operators
40J05 Summability in abstract structures
46A45 Sequence spaces

Keywords: spectrum of a linear operator; difference sequences; matrix mappings

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