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The fine spectra of the difference operator Δ over the sequence spaces 1 and bv. (English) Zbl 1119.47306
The authors prove statements concerning the spectrum of the difference operator of the form Δ=I-S, where S is the canonical shift operator in the sequence spaces 1 and bv. The same has been done by A. M. Akhmedov and F. Baṣar [Demonstr. Math. 39, No. 3, 585–595 (2006; Zbl 1118.47303)] by considering Δ in the spaces p (1p<). Alas, all results of these papers are well-known.

MSC:
47B39Difference operators (operator theory)
47A10Spectrum and resolvent of linear operators
47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)