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On the fine spectra of the difference operator $$\Delta$$ over the sequence space $$\ell_p$$ $$(1\leq p<\infty)$$. (English) Zbl 1118.47303
The authors prove some results concerning the spectrum of operators of the form $$\Delta = T - S$$, where $$S$$ is the canonical shift operator in one of the spaces $$\ell_{p} \;(1 \leq p < \infty).$$ Unfortunately, all results of the paper are well known.

##### MSC:
 47A10 Spectrum, resolvent 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 47B39 Linear difference operators
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