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Zbl 1119.47306
The fine spectra of the difference operator $\Delta$ over the sequence spaces $\ell_1$ and $bv$.
(English)
[J] Int. Math. Forum 1, No. 21-24, 1153-1160 (2006). ISSN 1312-7594; ISSN 1314-7536/e

The authors prove statements concerning the spectrum of the difference operator of the form $\Delta = I - S$, where $S$ is the canonical shift operator in the sequence spaces $\ell_{1}$ and $bv$. The same has been done by {\it A.\,M.\thinspace Akhmedov} and {\it F.\,Baṣar} [Demonstr.\ Math.\ 39, No.\,3, 585--595 (2006; Zbl 1118.47303)] by considering $\Delta$ in the spaces $\ell_{p}$ $(1\leq p<\infty)$. Alas, all results of these papers are well-known.
[Petru A. Cojuhari (Kraków)]
MSC 2000:
*47B39 Difference operators (operator theory)
47A10 Spectrum and resolvent of linear operators
47B37 Operators on sequence spaces, etc.

Citations: Zbl 1118.47303

Cited in: Zbl 1152.47024

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