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The fine spectra of the difference operator \(\Delta\) over the sequence space \(bv_p\), \((1\leq p<\infty)^*\). (English) Zbl 1134.47025

The authors find the spectrum of the operator \(\Delta = I - S\) acting on the sequence space \(b v_{p}\) (\(1 \leq p < \infty\)), \(S\) being the canonical translation operator on \(b v_{p}\).

MSC:

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