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On the fine spectrum of the difference operator \(\Delta\) on \(c_{0}\) and \(c\). (English) Zbl 1085.47041

The authors use the methods of functional analysis to study the spectrum of the difference operator \(\Delta\) (\(\Delta x_k:=x_k-x_{k-1}\)) represented by the associated infinite two-diagonal matrix.

MSC:

47B39 Linear difference operators
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
46B45 Banach sequence spaces
39A70 Difference operators
47A10 Spectrum, resolvent
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References:

[1] A.M. Akhmedov, F. Başar, On the fine spectrum of the Cesàro operator in \(c_0\); A.M. Akhmedov, F. Başar, On the fine spectrum of the Cesàro operator in \(c_0\)
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[10] Yıldırım, M., On the spectrum and fine spectrum of the compact Rhally operators, Indian J. Pure Appl. Math, 27, 8, 779-784 (1996) · Zbl 0859.47004
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