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Zbl 1139.47005
Bilgiç, Hüseyin; Furkan, Hasan
On the fine spectrum of the generalized difference operator $B(r,s)$ over the sequence spaces $\ell _p$ and $bv_{p},(1<p<\infty$).
(English)
[J] Nonlinear Anal., Theory Methods Appl. 68, No. 3, A, 499-506 (2008). ISSN 0362-546X

It is well-known that the spectrum of the canonical shift operator $S$ in each of the spaces $l_{p}$, $m = l_{\infty}$, $c$, $c_{0}$ or $bv_{p}$ ($1 \leq p < \infty$) is the unit disk of the complex plane. Therefore, the spectrum of the operator $B(r,s)=sS-r$ (where $r,s$ are real numbers) is the set $\sigma (B (t,s)) = \{z \in \Bbb{C} : \vert z - r \vert \leq s\}$. This is the main result of the paper.
[Petru A. Cojuhari (Kraków)]
MSC 2000:
*47A10 Spectrum and resolvent of linear operators
47B37 Operators on sequence spaces, etc.

Keywords: spectrum of an operator; sequence spaces $l_p$ and $bv_p$

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